{
  "id": "2305.06953",
  "version": "v1",
  "published": "2023-05-11T16:27:13.000Z",
  "updated": "2023-05-11T16:27:13.000Z",
  "title": "Asymptotic behavior of generalized capacities with applications to eigenvalue perturbations: the higher dimensional case",
  "authors": [
    "Laura Abatangelo",
    "Corentin Léna",
    "Paolo Musolino"
  ],
  "comment": "39 pages",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "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 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-11T16:27:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "31C15",
      "31B10",
      "35B25",
      "35C20"
    ],
    "keywords": [
      "higher dimensional case",
      "asymptotic behavior",
      "eigenvalue perturbations",
      "generalized capacities",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}