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2018 Estimates for eigenvalues of Aharonov–Bohm operators with varying poles and non-half-integer circulation
Laura Abatangelo, Veronica Felli, Benedetta Noris, Manon Nys
Anal. PDE 11(7): 1741-1785 (2018). DOI: 10.2140/apde.2018.11.1741

Abstract

We study the behavior of eigenvalues of a magnetic Aharonov–Bohm operator with non-half-integer circulation and Dirichlet boundary conditions in a planar domain. As the pole is moving in the interior of the domain, we estimate the rate of the eigenvalue variation in terms of the vanishing order of the limit eigenfunction at the limit pole. We also provide an accurate blow-up analysis for scaled eigenfunctions and prove a sharp estimate for their rate of convergence.

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Laura Abatangelo. Veronica Felli. Benedetta Noris. Manon Nys. "Estimates for eigenvalues of Aharonov–Bohm operators with varying poles and non-half-integer circulation." Anal. PDE 11 (7) 1741 - 1785, 2018. https://doi.org/10.2140/apde.2018.11.1741

Information

Received: 7 July 2017; Revised: 5 December 2017; Accepted: 18 February 2018; Published: 2018
First available in Project Euclid: 15 January 2019

zbMATH: 1388.35134
MathSciNet: MR3810471
Digital Object Identifier: 10.2140/apde.2018.11.1741

Subjects:
Primary: 35B40, 35B44, 35J10, 35J75, 35P15

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 7 • 2018
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