{
  "id": "1408.4583",
  "version": "v1",
  "published": "2014-08-20T09:46:22.000Z",
  "updated": "2014-08-20T09:46:22.000Z",
  "title": "Defect of compactness in spaces of bounded variation",
  "authors": [
    "Adimurthi",
    "Cyril Tintarev"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Defect of compactness for non-compact imbeddings of Banach spaces can be expressed in the form of a profile decomposition. This paper extends the profile decomposition for Sobolev spaces proved by Solimini (AIHP 1995) to the non-reflexive case p=1. Since existence of concentration profiles relies on weak-star compactness, the corresponding result is set in a larger, conjugate, space of functions of bounded variation. We prove existence of minimizers for related inequalities and generalizations for to spaces of bounded variation on Lie groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-20T09:46:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B50",
      "46B99",
      "26B30",
      "46E35",
      "46N20",
      "35H20",
      "35J92"
    ],
    "keywords": [
      "bounded variation",
      "profile decomposition",
      "concentration profiles relies",
      "paper extends",
      "non-compact imbeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4583A"
    }
  }
}