{
  "id": "1603.08663",
  "version": "v1",
  "published": "2016-03-29T07:21:43.000Z",
  "updated": "2016-03-29T07:21:43.000Z",
  "title": "On formulae decoupling the total variation of BV functions",
  "authors": [
    "Augusto C. Ponce",
    "Daniel Spector"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "In this paper we prove several formulae that enable one to capture the singular portion of the measure derivative of a function of bounded variation as a limit of non-local functionals. One special case shows that rescalings of the fractional Laplacian of a function $u\\in SBV$ converge strictly to the singular portion of $Du$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-29T07:21:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bv functions",
      "total variation",
      "formulae decoupling",
      "singular portion",
      "non-local functionals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}