{
  "id": "1210.6473",
  "version": "v1",
  "published": "2012-10-24T09:56:53.000Z",
  "updated": "2012-10-24T09:56:53.000Z",
  "title": "Compactness of special functions of bounded higher variation",
  "authors": [
    "Luigi Ambrosio",
    "Francesco Ghiraldin"
  ],
  "comment": "28 pages",
  "journal": "Analysis and Geometry in Metric Spaces, 2013, volume 1, 1-30",
  "doi": "10.2478/agms-2012-0001",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "Given an open set \\Omega\\subset\\R^m and n>1, we introduce the new spaces GB_nV(\\Omega) of Generalized functions of bounded higher variation and GSB_nV(\\Omega) of Generalized special functions of bounded higher variation that generalize, respectively, the space B_nV introduced by Jerrard and Soner and the corresponding SB_nV space studied by De Lellis. In this class of spaces, which allow the description of singularities of codimension n, the distributional jacobian Ju need not have finite mass: roughly speaking, finiteness of mass is not required for the (m-n)-dimensional part of Ju, but only finiteness of size. In the space GSB_nV we are able to provide compactness of sublevel sets and lower semicontinuity of Mumford-Shah type functionals, in the same spirit of the codimension 1 theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-24T09:56:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "49J45",
      "49Q15"
    ],
    "keywords": [
      "bounded higher variation",
      "compactness",
      "mumford-shah type functionals",
      "distributional jacobian ju",
      "generalized special functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6473A"
    }
  }
}