{
  "id": "1806.09945",
  "version": "v1",
  "published": "2018-06-26T12:43:37.000Z",
  "updated": "2018-06-26T12:43:37.000Z",
  "title": "The Monge-Ampère Equation",
  "authors": [
    "Connor Mooney"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this survey article we discuss the interior and boundary regularity of Alexandrov solutions to $\\det D^2u = 1$. We include some topics which it seems were not recently revisited in similar articles, including Calabi's interior $C^3$ estimate, and the approaches of Cheng-Yau and Lions to obtain classical solutions to the Dirichlet problem. The survey grew from two mini-courses given by the author in May 2018. One was for \"Advanced Lectures in Nonlinear Analysis\" at l'Universit\\`{a} degli Studi di Torino, and the other for the Oxford PDE CDT.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-26T12:43:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monge-ampère equation",
      "degli studi di torino",
      "oxford pde cdt",
      "nonlinear analysis",
      "similar articles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}