{
  "id": "1311.6795",
  "version": "v2",
  "published": "2013-11-26T20:20:23.000Z",
  "updated": "2013-12-13T10:46:36.000Z",
  "title": "Regularity of the $p$-Poisson equation in the plane",
  "authors": [
    "Erik Lindgren",
    "Peter Lindqvist"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the regularity of the $p$-Poisson equation $$ \\Delta_p u = h, \\quad h\\in L^q $$ in the plane. In the case $p>2$ and $2<q<\\infty$ we obtain the sharp H\\\"older exponent for the gradient. In the other cases we come arbitrarily close to the sharp exponent.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-13T10:46:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35J60",
      "35J70"
    ],
    "keywords": [
      "poisson equation",
      "regularity",
      "come arbitrarily close"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6795L"
    }
  }
}