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, Léna 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.
Asymptotic behavior of generalized capacities with applications to eigenvalue perturbations: The higher dimensional case
Corentin Lena;Paolo Musolino
2024
Abstract
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, Léna 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.
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