{
  "id": "math/0510577",
  "version": "v1",
  "published": "2005-10-26T20:06:06.000Z",
  "updated": "2005-10-26T20:06:06.000Z",
  "title": "Regularity of the distance function to the boundary",
  "authors": [
    "YanYan Li",
    "Louis Nirenberg"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Let $\\Omega$ be a domain in a smooth complete Finsler manifold, and let $G$ be the largest open subset of $\\Omega$ such that for every $x$ in $G$ there is a unique closest point from $\\partial \\Omega$ to $x$ (measured in the Finsler metric). We prove that the distance function from $\\partial \\Omega$ is in $C^{k,\\alpha}_{loc}(G\\cup \\partial \\Omega)$, $k\\ge 2$ and $0<\\alpha\\le 1$, if $\\partial \\Omega$ is in $C^{k,\\alpha}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-26T20:06:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53A05"
    ],
    "keywords": [
      "distance function",
      "regularity",
      "smooth complete finsler manifold",
      "largest open subset",
      "unique closest point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10577L"
    }
  }
}