{
  "id": "1604.08731",
  "version": "v1",
  "published": "2016-04-29T08:27:51.000Z",
  "updated": "2016-04-29T08:27:51.000Z",
  "title": "The Dirichlet problem for p-harmonic functions with respect to arbitrary compactifications",
  "authors": [
    "Anders Björn",
    "Jana Björn",
    "Tomas Sjödin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev-Perron solutions. We obtain various resolutivity and invariance results, and also show that most functions that have earlier been proved to be resolutive are in fact Sobolev-resolutive. We also introduce (Sobolev)-Wiener solutions and harmonizability in this nonlinear context, and study their connections to (Sobolev)-Perron solutions, partly using Q-compactifications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-29T08:27:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "30L99",
      "31C45",
      "35J66",
      "35J92",
      "49Q20"
    ],
    "keywords": [
      "p-harmonic functions",
      "arbitrary compactifications",
      "dirichlet problem",
      "perron method",
      "invariance problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}