{
  "id": "1010.0242",
  "version": "v3",
  "published": "2010-10-01T19:32:06.000Z",
  "updated": "2011-03-19T14:06:19.000Z",
  "title": "Lower semicontinuity and Young measures in BV without Alberti's Rank-One Theorem",
  "authors": [
    "Filip Rindler"
  ],
  "comment": "this is not a new version, just a fix for the previously wrongly compiled arXiv version",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We give a new proof of sequential weak* lower semicontinuity in $\\BV(\\Omega;\\R^m)$ for integral functionals with a quasiconvex Carath\\'{e}odory integrand with linear growth at infinity and such that the recession function $f^\\infty$ exists in a strong sense and is (jointly) continuous. In contrast to the classical proofs by Ambrosio & Dal Maso [J. Funct. Anal. 109 (1992), 76-97] and Fonseca & M\\\"{u}ller [Arch. Ration. Mech. Anal. 123 (1993), 1-49], we do not use Alberti's Rank-One Theorem [Proc. Roy. Soc. Edinburgh Sect. A} 123 (1993), 239-274], but a rigidity result for gradients. The proof is set in the framework of generalized Young measures and proceeds via establishing Jensen-type inequalities for regular and singular points of $Du$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-19T14:06:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "26B30",
      "28B05"
    ],
    "keywords": [
      "albertis rank-one theorem",
      "lower semicontinuity",
      "linear growth",
      "recession function",
      "strong sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.0242R"
    }
  }
}