{
  "id": "2208.10812",
  "version": "v1",
  "published": "2022-08-23T08:55:57.000Z",
  "updated": "2022-08-23T08:55:57.000Z",
  "title": "Representation formulas for pairings between divergence-measure fields and $BV$ functions",
  "authors": [
    "Giovanni E. Comi",
    "Graziano Crasta",
    "Virginia De Cicco",
    "Annalisa Malusa"
  ],
  "comment": "23 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "The purpose of this paper is to find pointwise representation formulas for the density of the pairing between divergence-measure fields and BV functions, in this way continuing the research started in [17,20]. In particular, we extend a representation formula from an unpublished paper of Anzellotti [7] involving the limit of cylindrical averages for normal traces, and we exploit a result of [35] in order to derive another representation in terms of limits of averages in half balls.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-23T08:55:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "26B20",
      "49Q15"
    ],
    "keywords": [
      "divergence-measure fields",
      "bv functions",
      "pointwise representation formulas",
      "normal traces",
      "half balls"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}