{
  "id": "0809.4174",
  "version": "v1",
  "published": "2008-09-24T12:38:04.000Z",
  "updated": "2008-09-24T12:38:04.000Z",
  "title": "On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone",
  "authors": [
    "Antoine Lemenant"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "We show that if $(u,K)$ is a global minimizer for the Mumford-Shah functional in $R^N$, and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degree 1/2. We deduce some applications in $R^3$ as for instance that an angular sector cannot be the singular set of a global minimizer, that if $K$ is a half-plane then $u$ is the corresponding cracktip function of two variables, or that if K is a cone that meets $S^2$ with an union of $C^1$ curvilinear convex polygones, then it is a $P$, $Y$ or $T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-24T12:38:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "49Q05",
      "35J25",
      "35P15"
    ],
    "keywords": [
      "global minimizer",
      "mumford-shah functional",
      "smooth cone",
      "homogeneity",
      "curvilinear convex polygones"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4174L"
    }
  }
}