Sharp boundary behavior of eigenvalues for Aharonov-Bohm operators with varying poles

被引：10

作者：

Abatangelo, Laura ^{[1
]}

Felli, Veronica ^{[2
]}

Noris, Benedetta ^{[3
]}

Nys, Manon ^{[4
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, Italy

[2] Univ Milano Bicocca, Dipartimento Sci Mat, Via Cozzi 55, I-20125 Milan, Italy

[3] Univ Libre Bruxelles, Dept Math, CP 214,Blvd Triomphe, B-1050 Brussels, Belgium

[4] Univ Turin, Dipartimento Matemat Giuseppe Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2017年 / 273卷 / 07期

关键词：

Aharonov-Bohm operators; Almgren monotonicity formula; Spectral theory; SPECTRAL MINIMAL PARTITIONS; NODAL SETS; SCHRODINGER-OPERATORS; MAGNETIC-FIELD; DOMAINS; THEOREM;

D O I：

10.1016/j.jfa.2017.06.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：2428 / 2487

页数：60

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