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

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 the results of Abatangelo et al. (2021); Abatangelo, Lena and Musolino (2022) 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. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).