{
  "id": "1811.12531",
  "version": "v1",
  "published": "2018-11-29T23:14:56.000Z",
  "updated": "2018-11-29T23:14:56.000Z",
  "title": "Global $W^{2,1+\\varepsilon}$ estimates for Monge-Ampère equation with natural boundary condition",
  "authors": [
    "Ovidiu Savin",
    "Hui Yu"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "For the Monge-Amp\\`ere equation with a right-hand side bounded away from 0 and infinity, we show that the solution, subject to the natural boundary condition arising in optimal transport, is in $W^{2,1+\\varepsilon}$ up to the boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-29T23:14:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monge-ampère equation",
      "right-hand side bounded away",
      "natural boundary condition arising",
      "optimal transport"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}