In this paper, we investigate the behavior of the eigenvalues of a magnetic Aharonov-Bohm operator with half-integer circulation and Dirichlet boundary conditions in a bounded planar domain. We establish a sharp relation between the rate of convergence of the eigenvalues as the singular pole is approaching a boundary point and the number of nodal lines of the eigenfunction of the limiting problem, i.e. of the Dirichlet-Laplacian, ending at that point. The proof relies on the construction of a limit profile depending on the direction along which the pole is moving, and on an Almgren-type monotonicity argument for magnetic operators
Abatangelo, L., Felli, V., Noris, B., & Nys, M. (2017). Sharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles. JOURNAL OF FUNCTIONAL ANALYSIS, 273(7), 2428-2487.
Citazione: | Abatangelo, L., Felli, V., Noris, B., & Nys, M. (2017). Sharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles. JOURNAL OF FUNCTIONAL ANALYSIS, 273(7), 2428-2487. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | Si |
Titolo: | Sharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles |
Autori: | Abatangelo, L; Felli, V; Noris, B; Nys, M |
Autori: | |
Data di pubblicazione: | 2017 |
Lingua: | English |
Rivista: | JOURNAL OF FUNCTIONAL ANALYSIS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jfa.2017.06.023 |
Appare nelle tipologie: | 01 - Articolo su rivista |
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