{
  "id": "1306.2704",
  "version": "v1",
  "published": "2013-06-12T03:40:01.000Z",
  "updated": "2013-06-12T03:40:01.000Z",
  "title": "Regularity for almost minimizers with free boundary",
  "authors": [
    "Guy David",
    "Tatiana Toro"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the local regularity of almost minimizers of the functional \\begin{equation*} J(u)=\\int_\\Omega |\\nabla u(x)|^2 +q^2_+(x)\\chi_{\\{u>0\\}}(x) +q^2_-(x)\\chi_{\\{u<0\\}}(x) \\end{equation*} where $q_\\pm \\in L^\\infty(\\Omega)$. Almost minimizers do not satisfy a PDE or a monotonicity formula like minimizers do (see \\cite{AC}, \\cite{ACF}, \\cite{CJK}, \\cite{W}). Nevertheless we succeed in proving that they are locally Lipschitz, which is the optimal regularity for minimizers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-12T03:40:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free boundary",
      "minimizers",
      "monotonicity formula",
      "optimal regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.2704D"
    }
  }
}