{
  "id": "1712.06315",
  "version": "v1",
  "published": "2017-12-18T09:50:45.000Z",
  "updated": "2017-12-18T09:50:45.000Z",
  "title": "Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and $RCD(K,\\infty)$ spaces",
  "authors": [
    "Luigi Ambrosio",
    "Elia Bruè",
    "Dario Trevisan"
  ],
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and $RCD(K, \\infty)$ spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-18T09:50:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C10",
      "60H07"
    ],
    "keywords": [
      "lipschitz functions",
      "lusin-type approximation",
      "non-doubling metric measure structures",
      "proof technique relies",
      "regular lagrangian flows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}