{
  "id": "1412.5747",
  "version": "v1",
  "published": "2014-12-18T08:03:54.000Z",
  "updated": "2014-12-18T08:03:54.000Z",
  "title": "Boundary $\\varepsilon$-regularity in optimal transportation",
  "authors": [
    "Shibing Chen",
    "Alessio Figalli"
  ],
  "comment": "24 pages, accepted by Advances in Mathematics",
  "categories": [
    "math.AP"
  ],
  "abstract": "We develop an $\\e$-regularity theory at the boundary for a general class of Monge-Amp\\`ere type equations arising in optimal transportation. As a corollary we deduce that optimal transport maps between H\\\"older densities supported on $C^2$ uniformly convex domains are $C^{1,\\alpha}$ up to the boundary, provided that the cost function is a sufficient small perturbation of the quadratic cost $-x\\cdot y$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-18T08:03:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal transportation",
      "sufficient small perturbation",
      "optimal transport maps",
      "quadratic cost",
      "general class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5747C"
    }
  }
}