{
  "id": "2106.13738",
  "version": "v1",
  "published": "2021-06-25T16:19:05.000Z",
  "updated": "2021-06-25T16:19:05.000Z",
  "title": "The Dirichlet problem for p-minimizers on finely open sets in metric spaces",
  "authors": [
    "Anders Björn",
    "Jana Björn",
    "Visa Latvala"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We initiate the study of fine $p$-(super)minimizers, associated with $p$-harmonic functions, on finely open sets in metric spaces, where $1 < p < \\infty$. After having developed their basic theory, we obtain the $p$-fine continuity of the solution of the Dirichlet problem on a finely open set with continuous Sobolev boundary values, as a by-product of similar pointwise results. These results are new also on unweighted $\\mathbf{R}^n$. We build this theory in a complete metric space equipped with a doubling measure supporting a $p$-Poincar\\'e inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-25T16:19:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "30L99",
      "31C40",
      "35J92"
    ],
    "keywords": [
      "finely open set",
      "dirichlet problem",
      "p-minimizers",
      "continuous sobolev boundary values",
      "complete metric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}