{
  "id": "1412.5964",
  "version": "v1",
  "published": "2014-12-18T17:42:50.000Z",
  "updated": "2014-12-18T17:42:50.000Z",
  "title": "Asymptotics of Hadamard Type for Eigenvalues of the Neumann Problem on $C^1$-domains for Elliptic Operators",
  "authors": [
    "Johan Thim"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1310.7967",
  "categories": [
    "math.AP"
  ],
  "abstract": "This article investigates how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain in the case when the domains involved are of class $C^1$. We consider the Laplacian and use results developed previously for the corresponding Lipschitz case. In contrast with the Lipschitz case however, in the $C^1$-case we derive an asymptotic formula for the eigenvalues when the domains are of class $C^1$. Moreover, as an application we consider the case of a $C^1$-perturbation when the reference domain is of class $C^{1,\\alpha}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-18T17:42:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P05",
      "47A75",
      "49R05",
      "47A55"
    ],
    "keywords": [
      "neumann problem",
      "hadamard type",
      "eigenvalues",
      "elliptic operator depend",
      "reference domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5964T"
    }
  }
}