{
  "id": "math/0702392",
  "version": "v1",
  "published": "2007-02-13T20:33:43.000Z",
  "updated": "2007-02-13T20:33:43.000Z",
  "title": "Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian",
  "authors": [
    "Luis Caffarelli",
    "Sandro Salsa",
    "Luis Silvestre"
  ],
  "doi": "10.1007/s00222-007-0086-6",
  "categories": [
    "math.AP"
  ],
  "abstract": "We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-13T20:33:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R35"
    ],
    "keywords": [
      "fractional laplacian",
      "free boundary",
      "apply local type arguments",
      "thin obstacle problem",
      "sharp regularity estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}