Asymptotic behavior of generalized capacities with applications to eigenvalue perturbations: the higher dimensional case

Laura Abatangelo, Corentin Léna, Paolo Musolino

Published 2023-05-11Version 1

We provide a full series expansion of a generalization of the so-called $u$-capacity related to the Dirichlet-Laplacian in dimension three and higher, extending previous results of the authors, and of the authors together with Virginie Bonnaillie-No\"el, dealing with the planar case. We apply the result in order to study the asymptotic behavior of perturbed eigenvalues when Dirichlet conditions are imposed on a small regular subset of the domain of the eigenvalue problem.