{
  "id": "1912.02247",
  "version": "v1",
  "published": "2019-12-04T20:55:28.000Z",
  "updated": "2019-12-04T20:55:28.000Z",
  "title": "Semiregular and strongly irregular boundary points for $p$-harmonic functions on unbounded sets in metric spaces",
  "authors": [
    "Anders Björn",
    "Daniel Hansevi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\\'e inequality, $1<p<\\infty$. We show that these are local properties. We also deduce several characterizations of semiregular points and strongly irregular points. In particular, semiregular points are characterized by means of capacity, $p$-harmonic measures, removability, and semibarriers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-04T20:55:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "30L99",
      "35J66",
      "35J92",
      "49Q20"
    ],
    "keywords": [
      "strongly irregular boundary points",
      "harmonic functions",
      "unbounded sets",
      "semiregular points",
      "complete metric spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}