{
  "id": "1705.02253",
  "version": "v1",
  "published": "2017-05-05T15:12:03.000Z",
  "updated": "2017-05-05T15:12:03.000Z",
  "title": "Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces",
  "authors": [
    "Anders Björn",
    "Jana Björn"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $X$ be a noncomplete metric space satisfying the usual (local) assumptions of a doubling property and a Poincar\\'e inequality. We study extensions of Newtonian Sobolev functions to the completion $\\widehat{X}$ of $X$ and use them to obtain several results on $X$ itself, in particular concerning minimal weak upper gradients, Lebesgue points, quasicontinuity, regularity properties of the capacity and better Poincar\\'e inequalities. We also provide a discussion about possible applications of the completions and extension results to $p$-harmonic functions on noncomplete spaces and show by examples that this is a rather delicate issue opening for various interpretations and new investigations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-05T15:12:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31E05",
      "30L99",
      "31C45",
      "35J60",
      "46E35"
    ],
    "keywords": [
      "noncomplete metric space",
      "newtonian sobolev functions",
      "poincare inequality",
      "concerning minimal weak upper gradients",
      "better poincare inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}