{
  "id": "1307.7079",
  "version": "v1",
  "published": "2013-07-26T15:48:55.000Z",
  "updated": "2013-07-26T15:48:55.000Z",
  "title": "Mean value formulas for solutions of some degenerate elliptic equations and applications",
  "authors": [
    "Hugo Aimar",
    "Gastón Beltritti",
    "Ivana Gómez"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a mean value formula for weak solutions of $div(|y|^{a}\\grad u)=0$ in $\\mathbb{R}^{n+1}=\\{(x,y): x\\in\\mathbb{R}^{n}, y\\in\\mathbb{R}\\}$, $-1<a<1$ and balls centered at points of the form $(x,0)$. We obtain an explicit nonlocal kernel for the mean value formula for solutions of $(-\\triangle)^{s}f=0$ on a domain $D$ of $\\mathbb{R}^{n}$. When $D$ is Lipschitz we prove a Besov type regularity improvement for the solutions of $(-\\triangle)^{s}f=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-26T15:48:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "35J70",
      "35B65",
      "46E35"
    ],
    "keywords": [
      "mean value formula",
      "degenerate elliptic equations",
      "applications",
      "besov type regularity improvement",
      "explicit nonlocal kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7079A"
    }
  }
}