{
  "id": "1905.04798",
  "version": "v1",
  "published": "2019-05-12T22:07:24.000Z",
  "updated": "2019-05-12T22:07:24.000Z",
  "title": "Boundary regularity for $p$-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces",
  "authors": [
    "Anders Björn",
    "Daniel Hansevi"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The theory of boundary regularity for $p$-harmonic functions is extended to unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\\'e inequality, $1<p<\\infty$. The barrier classification of regular boundary points is established, and it is shown that regularity is a local property of the boundary. We also obtain boundary regularity results for solutions of the obstacle problem on open sets, and characterize regularity further in several other ways.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-12T22:07:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "30L99",
      "35J66",
      "35J92",
      "49Q20"
    ],
    "keywords": [
      "harmonic functions",
      "obstacle problem",
      "unbounded sets",
      "open sets",
      "regular boundary points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}