{
  "id": "1304.2415",
  "version": "v1",
  "published": "2013-04-08T20:36:35.000Z",
  "updated": "2013-04-08T20:36:35.000Z",
  "title": "Monge-Ampere equation on exterior domains",
  "authors": [
    "Jiguang Bao",
    "Haigang Li",
    "Lei Zhang"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Monge-Amp\\`ere equation $\\det(D^2u)=f$ where $f$ is a positive function in $\\mathbb R^n$ and $f=1+O(|x|^{-\\beta})$ for some $\\beta>2$ at infinity. If the equation is globally defined on $\\mathbb R^n$ we classify the asymptotic behavior of solutions at infinity. If the equation is defined outside a convex bounded set we solve the corresponding exterior Dirichlet problem. Finally we prove for $n\\ge 3$ the existence of global solutions with prescribed asymptotic behavior at infinity. The assumption $\\beta>2$ is sharp for all the results in this article.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-08T20:36:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J96",
      "35J67"
    ],
    "keywords": [
      "exterior domains",
      "monge-ampere equation",
      "corresponding exterior dirichlet problem",
      "convex bounded set",
      "prescribed asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2415B"
    }
  }
}