{
  "id": "2009.10102",
  "version": "v1",
  "published": "2020-09-21T18:02:16.000Z",
  "updated": "2020-09-21T18:02:16.000Z",
  "title": "Note on an elementary inequality and its application to the regularity of $p$-harmonic functions",
  "authors": [
    "Saara Sarsa"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Sobolev regularity of $p$-harmonic functions. We show that $|Du|^{\\frac{p-2+s}{2}}Du$ belongs to the Sobolev space $W^{1,2}_{loc}$, $s>-1-\\frac{p-1}{n-1}$, for any $p$-harmonic function $u$. The proof is based on an elementary inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-21T18:02:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic function",
      "elementary inequality",
      "application",
      "sobolev regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}