{
  "id": "2107.10595",
  "version": "v1",
  "published": "2021-07-22T11:47:29.000Z",
  "updated": "2021-07-22T11:47:29.000Z",
  "title": "Two inequalities for the first Robin eigenvalue of the Finsler Laplacian",
  "authors": [
    "Giuseppina Di Blasio",
    "Nunzia Gavitone"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let \\Omega be a bounded connected, open set of \\R^n with Lipschitz boundary. Let F be a suitable norm in \\R^n and let \\Delta_F u be the so-colled Finsler Laplacian. In this paper we prove two inequalities for the first eigenvalue of \\Delta_F with Robin boundary conditions involving a positive function \\beta. As a consequence of our result we obtain the asymptotic behavior of this eigenvalue when \\beta is a positive constant which goes to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-22T11:47:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "35B40"
    ],
    "keywords": [
      "first robin eigenvalue",
      "inequalities",
      "robin boundary conditions",
      "asymptotic behavior",
      "so-colled finsler laplacian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}