{
  "id": "0810.0522",
  "version": "v2",
  "published": "2008-10-02T19:40:31.000Z",
  "updated": "2008-10-02T20:38:03.000Z",
  "title": "Boundary estimates for positive solutions to second order elliptic equations",
  "authors": [
    "Mikhail V. Safonov"
  ],
  "comment": "20 pages, 23 references",
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary and sufficient geometric conditions on the domain, which guarantee the Hopf-Oleinik type estimates and the boundary Lipschitz estimates for solutions. These conditions are sharp even for harmonic functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-10-02T20:38:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35J67",
      "35B05"
    ],
    "keywords": [
      "second order elliptic equations",
      "positive solutions",
      "boundary estimates",
      "boundary lipschitz estimates",
      "hopf-oleinik type estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0522S"
    }
  }
}