{
  "id": "1508.01362",
  "version": "v1",
  "published": "2015-08-06T11:04:33.000Z",
  "updated": "2015-08-06T11:04:33.000Z",
  "title": "Convex integration for the Monge-Ampère equation in two dimensions",
  "authors": [
    "Marta Lewicka",
    "Mohammad Reza Pakzad"
  ],
  "comment": "31 pages, 1 figure",
  "categories": [
    "math.AP",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "This paper concerns the questions of flexibility and rigidity of solutions to the Monge-Amp\\`ere equation which arises as a natural geometrical constraint in prestrained nonlinear elasticity. In particular, we focus on degenerate i.e. \"flexible\" weak solutions that can be constructed through methods of convex integration \\`a la Nash \\& Kuiper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-06T11:04:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex integration",
      "monge-ampère equation",
      "dimensions",
      "weak solutions",
      "natural geometrical constraint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}