{
  "id": "2001.02196",
  "version": "v1",
  "published": "2020-01-07T17:47:23.000Z",
  "updated": "2020-01-07T17:47:23.000Z",
  "title": "Uniqueness for a system of Monge-Ampère equations",
  "authors": [
    "Nam Q. Le"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note, we prove a uniqueness result, up to a positive multiplicative constant, for nontrivial convex solutions to a system of Monge-Amp\\`ere equations \\begin{equation*} \\left\\{ \\begin{alignedat}{2} \\det D^2 u~& = \\gamma |v|^p~&&\\text{in} ~ \\Omega, \\\\\\ \\det D^2 v~& = \\mu |u|^{n^2/p}~&&\\text{in} ~ \\Omega, \\\\\\ u=v &= 0~&&\\text{on}~ \\partial\\Omega \\end{alignedat} \\right. \\end{equation*} on bounded, smooth and uniformly convex domains $\\Omega\\subset R^n$ provided that $p$ is close to $n\\geq 2$. When $p=n$, we show that the uniqueness holds for general bounded convex domains $\\Omega\\subset R^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-07T17:47:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monge-ampère equations",
      "general bounded convex domains",
      "nontrivial convex solutions",
      "uniformly convex domains",
      "uniqueness result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}