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Estimates for
eigenvalues of Aharonov–Bohm operators with varying poles and
non-half-integer circulation
Laura Abatangelo, Veronica Felli, Benedetta Noris and Manon Nys |
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Vol. 11 (2018), No. 7, 1741–1785
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Abstract |
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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. |
Keywords
Aharonov–Bohm operators, Almgren monotonicity formula,
spectral theory
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Mathematical Subject Classification 2010
Primary: 35B40, 35B44, 35J10, 35J75, 35P15
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Milestones
Received: 7 July 2017
Revised: 5 December 2017
Accepted: 18 February 2018
Published: 20 May 2018
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Authors |
| Laura Abatangelo | |
| Dipartimento di Matematica e
Applicazioni Università degli Studi di Milano-Bicocca Milano Italy |
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| Veronica Felli | |
| Dipartimento di Scienza dei
Materiali Università degli Studi di Milano-Bicocca Milano Italy |
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| Benedetta Noris | |
| Laboratoire Amiénois de Mathématique
Fondamentale et Appliquée Université de Picardie Jules Verne Amiens France |
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| Manon Nys | |
| Dipartimento di Matematica Giuseppe
Peano Università degli Studi di Torino Torino Italy |
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