{
  "id": "1202.5561",
  "version": "v3",
  "published": "2012-02-24T21:25:22.000Z",
  "updated": "2012-11-16T12:05:08.000Z",
  "title": "Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps",
  "authors": [
    "Guido De Philippis",
    "Alessio Figalli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The aim of this note is to show that Alexandrov solutions of the Monge-Ampere equation, with right hand side bounded away from zero and infinity, converge strongly in $W^{2,1}_{loc}$ if their right hand side converge strongly in $L^1_{loc}$. As a corollary we deduce strong $W^{1,1}_{loc}$ stability of optimal transport maps.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-11-16T12:05:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal transport maps",
      "strong sobolev convergence",
      "second order stability",
      "monge-ampere equation",
      "hand side bounded away"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5561D"
    }
  }
}