{
  "id": "1806.05532",
  "version": "v1",
  "published": "2018-06-14T13:32:23.000Z",
  "updated": "2018-06-14T13:32:23.000Z",
  "title": "Regularity results for the equation $u_{11}u_{22} = 1$",
  "authors": [
    "Connor Mooney",
    "Ovidiu Savin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the equation $u_{11}u_{22} = 1$ in $\\mathbb{R}^2$. Our results include an interior $C^2$ estimate, classical solvability of the Dirichlet problem, and the existence of non-quadratic entire solutions. We also construct global singular solutions to the analogous equation in higher dimensions. At the end we state some open questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-14T13:32:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regularity results",
      "construct global singular solutions",
      "non-quadratic entire solutions",
      "open questions",
      "dirichlet problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}