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

2016/05/31 by Laura Abatangelo, Abatangelo, Laura, Veronica Felli +5
Computer Science · Mathematics · #35B40 #35B44 #35J10 #35J75 #35P15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1605.09569

openalex publication_date 2016/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the behavior of the eigenvalues of a magnetic\nAharonov-Bohm operator with half-integer circulation and Dirichlet boundary\nconditions in a bounded planar domain. We establish a sharp relation between\nthe rate of convergence of the eigenvalues as the singular pole is approaching\na boundary point and the number of nodal lines of the eigenfunction of the\nlimiting problem, i.e. of the Dirichlet Laplacian, ending at that point. The\nproof relies on the construction of a limit profile depending on the direction\nalong which the pole is moving, and on an Almgren-type monotonicity argument\nfor magnetic operators.\n

Related

• Sharp asymptotic estimates for eigenvalues of Aharonov-Bohm operators with varying poles
• On the eigenvalues of Aharonov-Bohm operators with varying poles: pole approaching the boundary of the domain
• Rate of convergence for eigenfunctions of Aharonov-Bohm operators with a moving pole
• On the leading term of the eigenvalue variation for Aharonov-Bohm\n operators with a moving pole
• On multiple eigenvalues for Aharonov-Bohm operators in planar domains