{
  "id": "1710.09492",
  "version": "v1",
  "published": "2017-10-25T23:27:54.000Z",
  "updated": "2017-10-25T23:27:54.000Z",
  "title": "Approximation by mappings with singular Hessian minors",
  "authors": [
    "Zhuomin Liu",
    "Jan Malý",
    "Mohammad Reza Pakzad"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP",
    "math.DG",
    "math.FA"
  ],
  "abstract": "Let $\\Omega\\subset\\mathbb R^n$ be a Lipschitz domain. Given $1\\leq p<k\\leq n$ and any $u\\in W^{2,p}(\\Omega)$ belonging to the little H\\\"older class $c^{1,\\alpha}$, we construct a sequence $u_j$ in the same space with $\\operatorname{rank}D^2u_j<k$ almost everywhere such that $u_j\\to u$ in $C^{1,\\alpha}$ and weakly in $W^{2,p}$. This result is in strong contrast with known regularity behavior of functions in $W^{2,p}$, $p\\geq k$, satisfying the same rank inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-25T23:27:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B99",
      "46T10"
    ],
    "keywords": [
      "singular hessian minors",
      "approximation",
      "lipschitz domain",
      "strong contrast",
      "regularity behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}