ESTIMATES FOR EIGENVALUES OF AHARONOV-BOHM OPERATORS WITH VARYING POLES AND NON-HALF-INTEGER CIRCULATION

Laura Abatangelo (1) , Veronica Felli , Benedetta Noris (2) , Manon Nys (1, 3)

1 UNIMIB - Università degli Studi di Milano-Bicocca = University of Milano-Bicocca
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
3 Département de mathématiques Université Libre de Bruxelles

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.

Domaines: Mathématiques [math]

Laura Abatangelo, Veronica Felli, Benedetta Noris, Manon Nys. ESTIMATES FOR EIGENVALUES OF AHARONOV-BOHM OPERATORS WITH VARYING POLES AND NON-HALF-INTEGER CIRCULATION. Analysis & PDE, 2018, 11 (7), pp.1741-1785. ⟨10.2140/apde.2018.11.1741⟩. ⟨hal-03623065⟩