{
  "id": "1702.04315",
  "version": "v1",
  "published": "2017-02-14T18:03:20.000Z",
  "updated": "2017-02-14T18:03:20.000Z",
  "title": "Optimal design problems for the first $p-$fractional eigenvalue with mixed boundary conditions",
  "authors": [
    "Julian Fernandez Bonder",
    "Julio D. Rossi",
    "Juan F. Spedaletti"
  ],
  "comment": "16 pages, submitted",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study an optimal shape design problem for the first eigenvalue of the fractional $p-$laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is restricted to have measure equal than a prescribed quantity, $\\alpha$). We show existence of an optimal design and analyze the asymptotic behavior when the fractional parameter $s\\uparrow 1$ obtaining asymptotic bounds that are independent of $\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-14T18:03:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P30",
      "35J92",
      "49R05"
    ],
    "keywords": [
      "mixed boundary conditions",
      "optimal design problems",
      "fractional eigenvalue",
      "optimal shape design problem",
      "first eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}