{
  "id": "1807.09497",
  "version": "v1",
  "published": "2018-07-25T09:26:14.000Z",
  "updated": "2018-07-25T09:26:14.000Z",
  "title": "Fine boundary regularity for the degenerate fractional $p$-Laplacian",
  "authors": [
    "Antonio Iannizzotto",
    "Sunra Mosconi",
    "Marco Squassina"
  ],
  "comment": "38 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $p\\ge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $\\Omega$. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution $u$ of such equation exhibits a weighted H\\\"older regularity up to the boundary, that is, $u/d^s\\in C^\\alpha(\\overline\\Omega)$ for some $\\alpha\\in(0,1)$, $d$ being the distance from the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-25T09:26:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D10",
      "35R11",
      "47G20"
    ],
    "keywords": [
      "fine boundary regularity",
      "degenerate fractional",
      "nonlocal superposition principle",
      "pseudo-differential equation driven",
      "dirichlet type conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}