{
  "id": "0904.1674",
  "version": "v1",
  "published": "2009-04-10T10:19:01.000Z",
  "updated": "2009-04-10T10:19:01.000Z",
  "title": "Pathological solutions to elliptic problems in divergence form with continuous coefficients",
  "authors": [
    "Tianling Jin",
    "Vladimir Maz'ya",
    "Jean Van Schaftingen"
  ],
  "comment": "6 pages",
  "journal": "C. R. Math. Acad. Sci. Paris 347 (2009), no. 13-14, 773-778",
  "doi": "10.1016/j.crma.2009.05.008",
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct a function $u \\in W^{1,1}_{\\mathrm{loc}} (B(0,1))$ which is a solution to $\\Div (A \\nabla u)=0$ in the sense of distributions, where $A$ is continuous and $u \\not \\in W^{1,p}_{\\mathrm{loc}} (B(0,1))$ for $p > 1$. We also give a function $u \\in W^{1,1}_{\\mathrm{loc}} (B(0,1))$ such that $u \\in W^{1,p}_{\\mathrm{loc}}(B(0,1))$ for every $p < \\infty$, $u$ satisfies $\\Div (A \\nabla u)=0$ with $A$ continuous but $u \\not \\in W^{1, \\infty}_{\\mathrm{loc}}(B(0,1))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-10T10:19:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D10"
    ],
    "keywords": [
      "divergence form",
      "elliptic problems",
      "continuous coefficients",
      "pathological solutions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1674J"
    }
  }
}