{
  "id": "0907.1250",
  "version": "v2",
  "published": "2009-07-07T16:11:44.000Z",
  "updated": "2014-02-25T18:05:34.000Z",
  "title": "An existence result for the infinity laplacian with non-homogeneous Neumann boundary conditions using Tug-of-War games",
  "authors": [
    "Fernando Charro",
    "Jesus Garcia Azorero",
    "Julio D. Rossi"
  ],
  "comment": "This paper has been withdrawn due to some errors in some of the proofs",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we show how to use a Tug-of-War game to obtain existence of a viscosity solution to the infinity laplacian with non-homogeneous mixed boundary conditions. For a Lipschitz and positive function $g$ there exists a viscosity solution of the mixed boundary value problem, $$ \\{\\begin{array}{ll} \\displaystyle -\\Delta_{\\infty}u(x)=0\\quad & \\text{in} \\Omega, \\displaystyle \\frac{\\partial u}{\\partial n}(x)= g (x)\\quad & \\text{on} \\Gamma_N, \\displaystyle u(x)= 0 \\quad & \\text{on} \\Gamma_D. \\end{array}. $$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-25T18:05:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "91A05",
      "49L25",
      "35J25"
    ],
    "keywords": [
      "non-homogeneous neumann boundary conditions",
      "tug-of-war game",
      "infinity laplacian",
      "existence result",
      "viscosity solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.1250C"
    }
  }
}