{
  "id": "1910.03541",
  "version": "v1",
  "published": "2019-10-08T16:55:50.000Z",
  "updated": "2019-10-08T16:55:50.000Z",
  "title": "Global $C^{2,α}$ estimates for the Monge-Ampère equation on polygonal domains in the plane",
  "authors": [
    "Nam Q. Le",
    "Ovidiu Savin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We classify global solutions of the Monge-Amp\\`ere equation $\\det D^2 u=1 $ on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^{2,\\alpha}$ estimates for the non-degenerate Monge-Amp\\`ere equation in convex polygonal domains in $\\mathbb R^2$ provided a globally $C^2$, convex strict subsolution exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-08T16:55:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monge-ampère equation",
      "quadratic boundary data",
      "convex polygonal domains",
      "convex strict subsolution",
      "classify global solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}