{
  "id": "1712.06807",
  "version": "v1",
  "published": "2017-12-19T07:59:15.000Z",
  "updated": "2017-12-19T07:59:15.000Z",
  "title": "The tusk condition and Petrovski criterion for the normalized $p\\mspace{1mu}$-parabolic equation",
  "authors": [
    "Anders Björn",
    "Jana Björn",
    "Mikko Parviainen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study boundary regularity for the normalized $p\\mspace{1mu}$-parabolic equation in arbitrary bounded domains. Effros and Kazdan (Indiana Univ. Math. J. 20 (1970), 683-693) showed that the so-called tusk condition guarantees regularity for the heat equation. We generalize this result to the normalized $p\\mspace{1mu}$-parabolic equation, and also obtain H\\\"older continuity. The tusk condition is a parabolic version of the exterior cone condition. We also obtain a sharp Petrovski criterion for the regularity of the latest moment of a domain. This criterion implies that the regularity of a boundary point is affected if one side of the equation is multiplied by a constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-19T07:59:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K61",
      "35B30",
      "35B51",
      "35D40",
      "35K92"
    ],
    "keywords": [
      "parabolic equation",
      "tusk condition guarantees regularity",
      "study boundary regularity",
      "sharp petrovski criterion",
      "exterior cone condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}