Spectral stability under removal of small capacity sets and applications to Aharonov-Bohm operators

2016/11/21 by Abatangelo, Laura, Felli, Veronica, Hillairet, Luc +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.06750

Abstract

We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov-Bohm operators with two colliding poles moving on an axis of symmetry of the domain.

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• Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle

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