{
  "id": "1111.7207",
  "version": "v2",
  "published": "2011-11-30T15:30:21.000Z",
  "updated": "2012-04-14T16:50:47.000Z",
  "title": "$W^{2,1}$ regularity for solutions of the Monge-Ampère equation",
  "authors": [
    "Guido De Philippis",
    "Alessio Figalli"
  ],
  "comment": "12 pages, no figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\\`ere equation, with right hand side bounded away from zero and infinity, is $W_{\\rm loc}^{2,1}$. This is obtained by showing higher integrability a-priori estimates for $D^2 u$, namely $D^2 u \\in L\\log^k L$ for any $k\\in \\mathbb N$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-14T16:50:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monge-ampère equation",
      "regularity",
      "showing higher integrability a-priori estimates",
      "right hand side bounded away",
      "strictly convex alexandrov solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.7207D"
    }
  }
}