{
  "id": "1311.5955",
  "version": "v1",
  "published": "2013-11-23T04:03:09.000Z",
  "updated": "2013-11-23T04:03:09.000Z",
  "title": "The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces",
  "authors": [
    "Daniel Hansevi"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the obstacle problem for unbounded sets in a proper metric measure space supporting a (p,p)-Poincare inequality. We prove that there exists a unique solution. We also prove that if the measure is doubling and the obstacle is continuous, then the solution is continuous, and moreover p-harmonic in the set where it does not touch the obstacle. This includes, as a special case, the solution of the Dirichlet problem for p-harmonic functions with Sobolev type boundary data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-23T04:03:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "31C45",
      "35D30",
      "35J20",
      "35J25",
      "35J60",
      "47J20",
      "49J40",
      "49J52",
      "49Q20",
      "58J05",
      "58J32"
    ],
    "keywords": [
      "dirichlet problems",
      "p-harmonic functions",
      "unbounded sets",
      "metric spaces",
      "metric measure space supporting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.5955H"
    }
  }
}