{
  "id": "1603.09647",
  "version": "v1",
  "published": "2016-03-31T15:44:24.000Z",
  "updated": "2016-03-31T15:44:24.000Z",
  "title": "Regularity of solutions for a free boundary problem in two dimensions",
  "authors": [
    "Mark Allen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the regularity of minimizers to the functional \\[ J(w)=\\int_{\\Omega} a^{ij}w_iw_j + Q\\chi_{\\{w>0\\}}, \\] over a bounded domain $\\Omega$ and among the class of nonnegative functions in $W^{1,2}(\\Omega)$ with prescribed boundary data. We assume that the coefficients $a^{ij}$ are only bounded and measurable and satisfy an ellipticity in condition. In two dimensions we prove that minimizers are H\\\"older continuous on subdomains. We also prove that in two dimensions a minimizer $u$ satisfies a linear growth condition from above and below near the free boundary $\\partial \\{u>0\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-31T15:44:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N60",
      "35R35",
      "35J15"
    ],
    "keywords": [
      "free boundary problem",
      "dimensions",
      "regularity",
      "linear growth condition",
      "prescribed boundary data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}