{
  "id": "2007.12479",
  "version": "v1",
  "published": "2020-07-24T12:23:23.000Z",
  "updated": "2020-07-24T12:23:23.000Z",
  "title": "A Remark on Monge-Ampère equation over exterior domains",
  "authors": [
    "Guanghao Hong"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We improve the result of Caffarelli-Li [CL03] on the asymptotic behavior at infinity of the exterior solution $u$ to Monge-Amp\\`{e}re equation $det(D^2u)=1$ on $\\mathbb{R}^n\\backslash K$ for $n\\geq 3$. We prove that the error term $O(|x|^{2-n})$ can be refined to $d (\\sqrt{x'Ax})^{2-n}+O(|x|^{1-n})$ with $d=Res[u]$ the residue of $u$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-24T12:23:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J96"
    ],
    "keywords": [
      "monge-ampère equation",
      "exterior domains",
      "asymptotic behavior",
      "exterior solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}