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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Bosch, H"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.02462">arXiv:2403.02462</a> <span> [<a href="https://arxiv.org/pdf/2403.02462">pdf</a>, <a href="https://arxiv.org/format/2403.02462">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Materials Science">cond-mat.mtrl-sci</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Spectral Theory">math.SP</span> </div> </div> <p class="title is-5 mathjax"> Edge states for tight-binding operators with soft walls </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Araya%2C+C+G">Camilo G贸mez Araya</a>, <a href="/search/math?searchtype=author&query=Gontier%2C+D">David Gontier</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.02462v1-abstract-short" style="display: inline;"> We study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape in this direction (the soft wall). We prove that a spectral flow appears in these corresponding edge models, as the wall is shifted. We identity this flow as a number of Bloch bands, and provide a lower bound for the num… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.02462v1-abstract-full').style.display = 'inline'; document.getElementById('2403.02462v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.02462v1-abstract-full" style="display: none;"> We study one- and two-dimensional periodic tight-binding models under the presence of a potential that grows to infinity in one direction, hence preventing the particles to escape in this direction (the soft wall). We prove that a spectral flow appears in these corresponding edge models, as the wall is shifted. We identity this flow as a number of Bloch bands, and provide a lower bound for the number of edge states appearing in such models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.02462v1-abstract-full').style.display = 'none'; document.getElementById('2403.02462v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 81Q10; 58J30; 47A13; 35J10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2305.05749">arXiv:2305.05749</a> <span> [<a href="https://arxiv.org/pdf/2305.05749">pdf</a>, <a href="https://arxiv.org/format/2305.05749">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Astrophysics of Galaxies">astro-ph.GA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Spectral Theory">math.SP</span> </div> </div> <p class="title is-5 mathjax"> Spectrum of the linearized Vlasov--Poisson equation around steady states from galactic dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Moreno%2C+M">Matias Moreno</a>, <a href="/search/math?searchtype=author&query=Rioseco%2C+P">Paola Rioseco</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2305.05749v4-abstract-short" style="display: inline;"> We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of oscillating modes and estimate their number. Our method allows us to take into account an attractive external potential. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2305.05749v4-abstract-full" style="display: none;"> We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of oscillating modes and estimate their number. Our method allows us to take into account an attractive external potential. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2305.05749v4-abstract-full').style.display = 'none'; document.getElementById('2305.05749v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 April, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 May, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">23 pages, 3 figures. v4: Introduction improved, references added, typos corrected. The main results are unchanged</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35Q83; 35Q85; 35P15; 70K20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2210.03091">arXiv:2210.03091</a> <span> [<a href="https://arxiv.org/pdf/2210.03091">pdf</a>, <a href="https://arxiv.org/format/2210.03091">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Dolbeault%2C+J">Jean Dolbeault</a>, <a href="/search/math?searchtype=author&query=Gontier%2C+D">David Gontier</a>, <a href="/search/math?searchtype=author&query=Pizzichillo%2C+F">Fabio Pizzichillo</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2210.03091v2-abstract-short" style="display: inline;"> We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart for Dirac operators of the Keller estimates for the Schr枚dinger operator, which are equivalent to Gagliardo-Nirenberg-Sobolev interpolation inequalities. Domain, self-adjointness, optimality and critical values of the nor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.03091v2-abstract-full').style.display = 'inline'; document.getElementById('2210.03091v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.03091v2-abstract-full" style="display: none;"> We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart for Dirac operators of the Keller estimates for the Schr枚dinger operator, which are equivalent to Gagliardo-Nirenberg-Sobolev interpolation inequalities. Domain, self-adjointness, optimality and critical values of the norms are addressed, while the optimal potential is given by a Dirac equation with a Kerr nonlinearity. A new critical bound appears, which is the smallest value of the norm of the potential for which eigenvalues may reach the bottom of the gap in the essential spectrum. The Keller estimate is then extended to a Lieb-Thirring inequality for the eigenvalues in the gap. Most of our result are established in the Birman-Schwinger reformulation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.03091v2-abstract-full').style.display = 'none'; document.getElementById('2210.03091v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 81Q10; 49R05; 49J35; 47A75; 47B25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.07019">arXiv:2201.07019</a> <span> [<a href="https://arxiv.org/pdf/2201.07019">pdf</a>, <a href="https://arxiv.org/format/2201.07019">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1063/5.0091016">10.1063/5.0091016 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Mixing in an anharmonic potential well </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Moreno%2C+M">Mat铆as Moreno</a>, <a href="/search/math?searchtype=author&query=Rioseco%2C+P">Paola Rioseco</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.07019v2-abstract-short" style="display: inline;"> We prove phase-space mixing for solutions to Liouville's equation for integrable systems. Under a natural non-harmonicity condition, we obtain weak convergence of the distribution function with rate $\langle \mathrm{time} \rangle^{-1}$. In one dimension, we also study the case where this condition fails at a certain energy, showing that mixing still holds but with a slower rate. When the condition… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.07019v2-abstract-full').style.display = 'inline'; document.getElementById('2201.07019v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.07019v2-abstract-full" style="display: none;"> We prove phase-space mixing for solutions to Liouville's equation for integrable systems. Under a natural non-harmonicity condition, we obtain weak convergence of the distribution function with rate $\langle \mathrm{time} \rangle^{-1}$. In one dimension, we also study the case where this condition fails at a certain energy, showing that mixing still holds but with a slower rate. When the condition holds and functions have higher regularity, the rate can be faster. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.07019v2-abstract-full').style.display = 'none'; document.getElementById('2201.07019v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 1 figure. v2:additional result in Theorem 1.3, typos corrected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 82C70 (Primary) 35Q49; 82C40 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.12413">arXiv:2110.12413</a> <span> [<a href="https://arxiv.org/pdf/2110.12413">pdf</a>, <a href="https://arxiv.org/ps/2110.12413">ps</a>, <a href="https://arxiv.org/format/2110.12413">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Spectral Theory">math.SP</span> </div> </div> <p class="title is-5 mathjax"> CR embeddability of quotients of the Rossi sphere via spectral theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bosch%2C+H">Henry Bosch</a>, <a href="/search/math?searchtype=author&query=Gonzales%2C+T">Tyler Gonzales</a>, <a href="/search/math?searchtype=author&query=Spinelli%2C+K">Kamryn Spinelli</a>, <a href="/search/math?searchtype=author&query=Udell%2C+G">Gabe Udell</a>, <a href="/search/math?searchtype=author&query=Zeytuncu%2C+Y+E">Yunus E. Zeytuncu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.12413v1-abstract-short" style="display: inline;"> We look at the action of finite subgroups of $\operatorname{SU}(2)$ on $S^3$, viewed as a CR manifold, both with the standard CR structure as the unit sphere in $\mathbb{C}^2$ and with a perturbed CR structure known as the Rossi sphere. We show that quotient manifolds from these actions are indeed CR manifolds, and relate the order of the subgroup of $\operatorname{SU}(2)$ to the asymptotic distri… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.12413v1-abstract-full').style.display = 'inline'; document.getElementById('2110.12413v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.12413v1-abstract-full" style="display: none;"> We look at the action of finite subgroups of $\operatorname{SU}(2)$ on $S^3$, viewed as a CR manifold, both with the standard CR structure as the unit sphere in $\mathbb{C}^2$ and with a perturbed CR structure known as the Rossi sphere. We show that quotient manifolds from these actions are indeed CR manifolds, and relate the order of the subgroup of $\operatorname{SU}(2)$ to the asymptotic distribution of the Kohn Laplacian's eigenvalues on the quotient. We show that the order of the subgroup determines whether the quotient of the Rossi sphere by the action of that subgroup is CR embeddable. Finally, in the unperturbed case, we prove that we can determine the size of the subgroup by using the point spectrum. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.12413v1-abstract-full').style.display = 'none'; document.getElementById('2110.12413v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.11703">arXiv:2102.11703</a> <span> [<a href="https://arxiv.org/pdf/2102.11703">pdf</a>, <a href="https://arxiv.org/ps/2102.11703">ps</a>, <a href="https://arxiv.org/format/2102.11703">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s00220-023-04646-4">10.1007/s00220-023-04646-4 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Results on the spectral stability of standing wave solutions of the Soler model in 1-D </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Aldunate%2C+D">Danko Aldunate</a>, <a href="/search/math?searchtype=author&query=Ricaud%2C+J">Julien Ricaud</a>, <a href="/search/math?searchtype=author&query=Stockmeyer%2C+E">Edgardo Stockmeyer</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2102.11703v3-abstract-short" style="display: inline;"> We study the spectral stability of the nonlinear Dirac operator in dimension $1+1$, restricting our attention to nonlinearities of the form $f(\langle蠄,尾蠄\rangle_{\mathbb{C}^2}) 尾$. We obtain bounds on eigenvalues for the linearized operator around standing wave solutions of the form $e^{-i蠅t} 蠁_0$. For the case of power nonlinearities $f(s)= s |s|^{p-1}$, $p>0$, we obtain a range of frequencies… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.11703v3-abstract-full').style.display = 'inline'; document.getElementById('2102.11703v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.11703v3-abstract-full" style="display: none;"> We study the spectral stability of the nonlinear Dirac operator in dimension $1+1$, restricting our attention to nonlinearities of the form $f(\langle蠄,尾蠄\rangle_{\mathbb{C}^2}) 尾$. We obtain bounds on eigenvalues for the linearized operator around standing wave solutions of the form $e^{-i蠅t} 蠁_0$. For the case of power nonlinearities $f(s)= s |s|^{p-1}$, $p>0$, we obtain a range of frequencies $蠅$ such that the linearized operator has no unstable eigenvalues on the axes of the complex plane. As a crucial part of the proofs, we obtain a detailed description of the spectra of the self-adjoint blocks in the linearized operator. In particular, we show that the condition $\langle蠁_0,尾蠁_0\rangle_{\mathbb{C}^2} > 0$ characterizes groundstates analogously to the Schr枚dinger case. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.11703v3-abstract-full').style.display = 'none'; document.getElementById('2102.11703v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">45 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Communications in Mathematical Physics 401 (2023) 227--273 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2010.04568">arXiv:2010.04568</a> <span> [<a href="https://arxiv.org/pdf/2010.04568">pdf</a>, <a href="https://arxiv.org/ps/2010.04568">ps</a>, <a href="https://arxiv.org/format/2010.04568">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Spectral Theory">math.SP</span> </div> </div> <p class="title is-5 mathjax"> A Tauberian Approach to Weyl's Law for the Kohn Laplacian on Spheres </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bosch%2C+H">Henry Bosch</a>, <a href="/search/math?searchtype=author&query=Gonzales%2C+T">Tyler Gonzales</a>, <a href="/search/math?searchtype=author&query=Spinelli%2C+K">Kamryn Spinelli</a>, <a href="/search/math?searchtype=author&query=Udell%2C+G">Gabe Udell</a>, <a href="/search/math?searchtype=author&query=Zeytuncu%2C+Y+E">Yunus E. Zeytuncu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2010.04568v1-abstract-short" style="display: inline;"> We compute the leading coefficient in the asymptotic expansion of the eigenvalue counting function for the Kohn Laplacian on the spheres. We express the coefficient as an infinite sum and as an integral. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2010.04568v1-abstract-full" style="display: none;"> We compute the leading coefficient in the asymptotic expansion of the eigenvalue counting function for the Kohn Laplacian on the spheres. We express the coefficient as an infinite sum and as an integral. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.04568v1-abstract-full').style.display = 'none'; document.getElementById('2010.04568v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 32V05; 32V20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.01276">arXiv:2008.01276</a> <span> [<a href="https://arxiv.org/pdf/2008.01276">pdf</a>, <a href="https://arxiv.org/format/2008.01276">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Kowalczyk%2C+M">Micha艂 Kowalczyk</a>, <a href="/search/math?searchtype=author&query=Martel%2C+Y">Yvan Martel</a>, <a href="/search/math?searchtype=author&query=Mu%C3%B1oz%2C+C">Claudio Mu帽oz</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2008.01276v1-abstract-short" style="display: inline;"> We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \begin{equation*} \partial_t^2蠁-\partial_x^2蠁+ W'(蠁) = 0, \quad (t,x)\in\mathbb{R}\times\mathbb{R}. \end{equation*} The orbital stability of kinks under general assumptions on the potential $W$ is a consequence of energy arguments. Our main result is the derivation of a simple and explicit suffici… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.01276v1-abstract-full').style.display = 'inline'; document.getElementById('2008.01276v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.01276v1-abstract-full" style="display: none;"> We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \begin{equation*} \partial_t^2蠁-\partial_x^2蠁+ W'(蠁) = 0, \quad (t,x)\in\mathbb{R}\times\mathbb{R}. \end{equation*} The orbital stability of kinks under general assumptions on the potential $W$ is a consequence of energy arguments. Our main result is the derivation of a simple and explicit sufficient condition on the potential $W$ for the asymptotic stability of a given kink. This condition applies to any static or moving kink, in particular no symmetry assumption is required. Last, motivated by the Physics literature, we present applications of the criterion to the $P(蠁)_2$ theories and the double sine-Gordon theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.01276v1-abstract-full').style.display = 'none'; document.getElementById('2008.01276v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">76 pages, 2 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35L71; 35B40; 37K40 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.05010">arXiv:1902.05010</a> <span> [<a href="https://arxiv.org/pdf/1902.05010">pdf</a>, <a href="https://arxiv.org/format/1902.05010">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Self-Adjointness of two dimensional Dirac operators on corner domains </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Pizzichillo%2C+F">Fabio Pizzichillo</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.05010v2-abstract-short" style="display: inline;"> We investigate the self-adjointness of the two-dimensional Dirac operator $D$, with quantum-dot and Lorentz-scalar $未$-shell boundary conditions, on piecewise $C^2$ domains with finitely many corners. For both models, we prove the existence of a unique self-adjoint realization whose domain is included in the Sobolev space $H^{1/2}$, the formal form domain of the free Dirac operator. The main part… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.05010v2-abstract-full').style.display = 'inline'; document.getElementById('1902.05010v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.05010v2-abstract-full" style="display: none;"> We investigate the self-adjointness of the two-dimensional Dirac operator $D$, with quantum-dot and Lorentz-scalar $未$-shell boundary conditions, on piecewise $C^2$ domains with finitely many corners. For both models, we prove the existence of a unique self-adjoint realization whose domain is included in the Sobolev space $H^{1/2}$, the formal form domain of the free Dirac operator. The main part of our paper consists of a description of the domain of $D^*$ in terms of the domain of $D$ and the set of harmonic functions that verify some mixed boundary conditions. Then, we give a detailed study of the problem on an infinite sector, where explicit computations can be made: we find the self-adjoint extensions for this case. The result is then translated to general domains by a coordinate transformation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.05010v2-abstract-full').style.display = 'none'; document.getElementById('1902.05010v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1810.05698">arXiv:1810.05698</a> <span> [<a href="https://arxiv.org/pdf/1810.05698">pdf</a>, <a href="https://arxiv.org/format/1810.05698">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Existence and non-existence of minimizers for Poincar茅-Sobolev inequalities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Benguria%2C+R+D">Rafael D. Benguria</a>, <a href="/search/math?searchtype=author&query=Vallejos%2C+C">Crist贸bal Vallejos</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1810.05698v1-abstract-short" style="display: inline;"> In this paper we study the existence and non-existence of minimizers for a type of (critical) Poincar茅-Sobolev inequalities. We show that minimizers do exist for smooth domains in $\mathbb{R}^d$, an also for some polyhedral domains. On the other hand, we prove the non-existence of minimizers in the rectangular isosceles triangle in $\mathbb{R}^2$. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1810.05698v1-abstract-full" style="display: none;"> In this paper we study the existence and non-existence of minimizers for a type of (critical) Poincar茅-Sobolev inequalities. We show that minimizers do exist for smooth domains in $\mathbb{R}^d$, an also for some polyhedral domains. On the other hand, we prove the non-existence of minimizers in the rectangular isosceles triangle in $\mathbb{R}^2$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1810.05698v1-abstract-full').style.display = 'none'; document.getElementById('1810.05698v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 October, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">20 pages, 3 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1807.11690">arXiv:1807.11690</a> <span> [<a href="https://arxiv.org/pdf/1807.11690">pdf</a>, <a href="https://arxiv.org/ps/1807.11690">ps</a>, <a href="https://arxiv.org/format/1807.11690">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> A short proof of the ionization conjecture in M眉ller theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Frank%2C+R+L">Rupert L. Frank</a>, <a href="/search/math?searchtype=author&query=Nam%2C+P+T">Phan Th脿nh Nam</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+v+d">Hanne van den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1807.11690v1-abstract-short" style="display: inline;"> We prove that in M眉ller theory, a nucleus of charge $Z$ can bind at most $Z+C$ electrons for a constant $C$ independent of $Z$. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1807.11690v1-abstract-full" style="display: none;"> We prove that in M眉ller theory, a nucleus of charge $Z$ can bind at most $Z+C$ electrons for a constant $C$ independent of $Z$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1807.11690v1-abstract-full').style.display = 'none'; document.getElementById('1807.11690v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 July, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages; contribution to the proceedings of the conference QMath 13</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1802.01740">arXiv:1802.01740</a> <span> [<a href="https://arxiv.org/pdf/1802.01740">pdf</a>, <a href="https://arxiv.org/ps/1802.01740">ps</a>, <a href="https://arxiv.org/format/1802.01740">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Gagliardo-Nirenberg-Sobolev inequalities for convex domains in $\mathbb{R}^d$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Benguria%2C+R+D">Rafael D. Benguria</a>, <a href="/search/math?searchtype=author&query=Vallejos%2C+C">Cristobal Vallejos</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1802.01740v2-abstract-short" style="display: inline;"> A special type of Gagliardo-Nirenberg-Sobolev (GNS) inequalities in $\mathbb{R}^d$ has played a key role in several proofs of Lieb-Thirring inequalities. Recently, a need for GNS inequalities in convex domains of $\mathbb{R}^d$, in particular for cubes, has arised. The purpose of this manuscript is two-fold. First we prove a GNS inequality for convex domains, with explicit constants which depend o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.01740v2-abstract-full').style.display = 'inline'; document.getElementById('1802.01740v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1802.01740v2-abstract-full" style="display: none;"> A special type of Gagliardo-Nirenberg-Sobolev (GNS) inequalities in $\mathbb{R}^d$ has played a key role in several proofs of Lieb-Thirring inequalities. Recently, a need for GNS inequalities in convex domains of $\mathbb{R}^d$, in particular for cubes, has arised. The purpose of this manuscript is two-fold. First we prove a GNS inequality for convex domains, with explicit constants which depend on the geometry of the domain. Later, using the discrete version of Rumin's method, we prove GNS inequalities on cubes with improved constants. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.01740v2-abstract-full').style.display = 'none'; document.getElementById('1802.01740v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 February, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 February, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, v2: typo in eq(9), p.3 fixed</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1608.05625">arXiv:1608.05625</a> <span> [<a href="https://arxiv.org/pdf/1608.05625">pdf</a>, <a href="https://arxiv.org/ps/1608.05625">ps</a>, <a href="https://arxiv.org/format/1608.05625">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> The maximal excess charge in M眉ller density-matrix-functional theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Frank%2C+R+L">Rupert L. Frank</a>, <a href="/search/math?searchtype=author&query=Nam%2C+P+T">Phan Th脿nh Nam</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1608.05625v1-abstract-short" style="display: inline;"> We consider an atom described by M眉ller theory, which is similar to Hartree-Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most Z+C electrons, where C is a universal constant. Our proof proceeds by comparison with Thomas-Fermi theory and a key ingredient is a novel bound on the number of electrons far from the nucleus. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1608.05625v1-abstract-full" style="display: none;"> We consider an atom described by M眉ller theory, which is similar to Hartree-Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most Z+C electrons, where C is a universal constant. Our proof proceeds by comparison with Thomas-Fermi theory and a key ingredient is a novel bound on the number of electrons far from the nucleus. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1608.05625v1-abstract-full').style.display = 'none'; document.getElementById('1608.05625v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 August, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">25 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1606.07355">arXiv:1606.07355</a> <span> [<a href="https://arxiv.org/pdf/1606.07355">pdf</a>, <a href="https://arxiv.org/ps/1606.07355">ps</a>, <a href="https://arxiv.org/format/1606.07355">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> The ionization conjecture in Thomas-Fermi-Dirac-von Weizs盲cker theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Frank%2C+R+L">Rupert L. Frank</a>, <a href="/search/math?searchtype=author&query=Nam%2C+P+T">Phan Th脿nh Nam</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1606.07355v2-abstract-short" style="display: inline;"> We prove that in Thomas-Fermi-Dirac-von Weizs盲cker theory, a nucleus of charge $Z>0$ can bind at most $Z+C$ electrons, where $C$ is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the partic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.07355v2-abstract-full').style.display = 'inline'; document.getElementById('1606.07355v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1606.07355v2-abstract-full" style="display: none;"> We prove that in Thomas-Fermi-Dirac-von Weizs盲cker theory, a nucleus of charge $Z>0$ can bind at most $Z+C$ electrons, where $C$ is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1606.07355v2-abstract-full').style.display = 'none'; document.getElementById('1606.07355v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 March, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 June, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Final version to appear in Comm. Pure Appl. Math</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1603.07368">arXiv:1603.07368</a> <span> [<a href="https://arxiv.org/pdf/1603.07368">pdf</a>, <a href="https://arxiv.org/format/1603.07368">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> </div> </div> <p class="title is-5 mathjax"> Nonexistence in Thomas-Fermi-Dirac-von Weizs盲cker theory with small nuclear charges </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Nam%2C+P+T">Phan Th脿nh Nam</a>, <a href="/search/math?searchtype=author&query=Bosch%2C+H+V+D">Hanne Van Den Bosch</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1603.07368v2-abstract-short" style="display: inline;"> We study the ionization problem in the Thomas-Fermi-Dirac-von Weizs盲cker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we ob… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1603.07368v2-abstract-full').style.display = 'inline'; document.getElementById('1603.07368v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1603.07368v2-abstract-full" style="display: none;"> We study the ionization problem in the Thomas-Fermi-Dirac-von Weizs盲cker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1603.07368v2-abstract-full').style.display = 'none'; document.getElementById('1603.07368v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 March, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Final version, to appear in Mathematical Physics, Analysis and Geometry. Minor clarifications and corrections, a figure added. 30 pages, 1 figure</span> </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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