{
  "id": "1109.6783",
  "version": "v1",
  "published": "2011-09-30T10:23:40.000Z",
  "updated": "2011-09-30T10:23:40.000Z",
  "title": "A sharp inequality for transport maps in W^{1,p}(R) via approximation",
  "authors": [
    "Jean Louet",
    "Filippo Santambrogio"
  ],
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "For $f$ convex and increasing, we prove the inequality $ \\int f(|U'|) \\geq \\int f(nT')$, every time that $U$ is a Sobolev function of one variable and $T$ is the non-decreasing map defined on the same interval with the same image measure as $U$, and the function $n(x)$ takes into account the number of pre-images of $U$ at each point. This may be applied to some variational problems in a mass-transport framework or under volume constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-30T10:23:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transport maps",
      "sharp inequality",
      "approximation",
      "mass-transport framework",
      "variational problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6783L"
    }
  }
}