{
  "id": "1907.08814",
  "version": "v1",
  "published": "2019-07-20T13:52:36.000Z",
  "updated": "2019-07-20T13:52:36.000Z",
  "title": "Sobolev versus Hölder minimizers for the degenerate fractional $p$-Laplacian",
  "authors": [
    "Antonio Iannizzotto",
    "Sunra Mosconi",
    "Marco Squassina"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a nonlinear pseudo-differential equation driven by the fractional $p$-Laplacian $(-\\Delta)^s_p$ with $s\\in(0,1)$ and $p\\ge 2$ (degenerate case), under Dirichlet type conditions in a smooth domain $\\Omega$. We prove that local minimizers of the associated energy functional in the fractional Sobolev space $W^{s,p}_0(\\Omega)$ and in the weighted H\\\"older space $C^0_s(\\overline\\Omega)$, respectively, do coincide.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-20T13:52:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D10",
      "35R11",
      "47G20"
    ],
    "keywords": [
      "degenerate fractional",
      "hölder minimizers",
      "nonlinear pseudo-differential equation driven",
      "fractional sobolev space",
      "dirichlet type conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}