{
  "id": "1809.08580",
  "version": "v1",
  "published": "2018-09-23T11:40:20.000Z",
  "updated": "2018-09-23T11:40:20.000Z",
  "title": "Hadamard Asymptotics for Eigenvalues of the Dirichlet Laplacian",
  "authors": [
    "Vladimir Kozlov",
    "Johan Thim"
  ],
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "This paper is dedicated to the classical Hadamard formula for asymptotics of eigenvalues of the Dirichlet-Laplacian under perturbations of the boundary. We prove that the Hadamard formula still holds for $C^1$-domains with $C^1$-perturbations. We also derive an optimal estimate for the remainder term in the $C^{1,\\alpha}$-case. Furthermore, if the boundary is merely Lipschitz, we show that the Hadamard formula is not valid.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-23T11:40:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P05",
      "47A75",
      "49R05",
      "47A55"
    ],
    "keywords": [
      "dirichlet laplacian",
      "hadamard asymptotics",
      "eigenvalues",
      "classical hadamard formula",
      "perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}