{
  "id": "1410.2228",
  "version": "v1",
  "published": "2014-10-08T19:37:18.000Z",
  "updated": "2014-10-08T19:37:18.000Z",
  "title": "Stability and continuity of functions of least gradient",
  "authors": [
    "Riikka Korte",
    "Panu Lahti",
    "Nageswari Shanmugalingam"
  ],
  "comment": "29 pages",
  "categories": [
    "math.MG",
    "math.AP",
    "math.OC"
  ],
  "abstract": "In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-08T19:37:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "31E99",
      "31C45",
      "26B15"
    ],
    "keywords": [
      "continuity",
      "metric measure spaces",
      "maximum principle",
      "gradient functions",
      "stability properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2228H"
    }
  }
}