{
  "id": "math/0609670",
  "version": "v2",
  "published": "2006-09-24T14:55:05.000Z",
  "updated": "2007-07-07T17:01:57.000Z",
  "title": "The Calderón-Zygmund theory for elliptic problems with measure data",
  "authors": [
    "Giuseppe Mingione"
  ],
  "journal": "Ann. Scu. Norm. Sup. Pisa Cl. Sci. (Ser. V) 6 (2007) 195-251",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider non-linear elliptic equations having a measure in the right hand side, of the type $ \\divo a(x,Du)=\\mu, $ and prove differentiability and integrability results for solutions. New estimates in Marcinkiewicz spaces are also given, and the impact of the measure datum density properties on the regularity of solutions is analyzed in order to build a suitable Calder\\'on-Zygmund theory for the problem. All the regularity results presented in this paper are provided together with explicit local a priori estimates.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-07-07T17:01:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D10"
    ],
    "keywords": [
      "elliptic problems",
      "calderón-zygmund theory",
      "measure datum density properties",
      "non-linear elliptic equations",
      "right hand side"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9670M"
    }
  }
}