Vol. 11, No. 7, 2018

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Estimates for eigenvalues of Aharonov–Bohm operators with varying poles and non-half-integer circulation

Laura Abatangelo, Veronica Felli, Benedetta Noris and Manon Nys

Vol. 11 (2018), No. 7, 1741–1785

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.

Aharonov–Bohm operators, Almgren monotonicity formula, spectral theory
Mathematical Subject Classification 2010
Primary: 35B40, 35B44, 35J10, 35J75, 35P15
Received: 7 July 2017
Revised: 5 December 2017
Accepted: 18 February 2018
Published: 20 May 2018
Laura Abatangelo
Dipartimento di Matematica e Applicazioni
Università degli Studi di Milano-Bicocca
Veronica Felli
Dipartimento di Scienza dei Materiali
Università degli Studi di Milano-Bicocca
Benedetta Noris
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
Université de Picardie Jules Verne
Manon Nys
Dipartimento di Matematica Giuseppe Peano
Università degli Studi di Torino