On Aharonov–Bohm Operators with Two Colliding Poles-Reference-Cited by-同舟云学术

On Aharonov–Bohm Operators with Two Colliding Poles

Published:2017-03-18 Issue:2 Volume:17 Page:283-296
ISSN:1536-1365
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Abatangelo Laura¹,Felli Veronica²,Léna Corentin³

Affiliation:

1. Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, Via Cozzi 55, 20125 Milano, Italy

2. Dipartimento di Scienza dei Materiali, Università di Milano–Bicocca, Via Cozzi 55, 20125 Milano, Italy

3. Dipartimento di Matematica Giuseppe Peano, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

Abstract

Abstract We consider Aharonov–Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction.

Funder

European Research Council

Ministero dell’Istruzione, dell’Università e della Ricerca

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2017-0004/pdf

Reference20 articles.

1. Abatangelo L. and Felli V., Sharp asymptotic estimates for eigenvalues of Aharonov–Bohm operators with varying poles, Calc. Var. Partial Differential Equations 54 (2015), no. 4, 3857–3903.

2. Abatangelo L. and Felli V., On the leading term of the eigenvalue variation for Aharonov–Bohm operators with a moving pole, SIAM J. Math. Anal. 48 (2016), no. 4, 2843–2868.

3. Abatangelo L., Felli V., Hillairet L. and Léna C., Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators, preprint 2016, https://arxiv.org/abs/1611.06750.

4. Abatangelo L., Felli V., Noris B. and Nys M., Sharp boundary behavior of eigenvalues for Aharonov–Bohm operators with varying poles, preprint 2016, https://arxiv.org/abs/1605.09569.

5. Alziary B., Fleckinger-Pellé J. and Takáč P., Eigenfunctions and Hardy inequalities for a magnetic Schrödinger operator in ℝ2${{\mathbb{R}}^{2}}$, Math. Methods Appl. Sci. 26 (2003), no. 13, 1093–1136.

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications;ESAIM: Control, Optimisation and Calculus of Variations;2020

2. Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators;Journal of Spectral Theory;2018-10-24

3. Multiple Aharonov–Bohm eigenvalues: The case of the first eigenvalue on the disk;Proceedings of the American Mathematical Society;2018-10-18

4. On multiple eigenvalues for Aharonov–Bohm operators in planar domains;Nonlinear Analysis;2018-04