{
  "id": "0910.5876",
  "version": "v2",
  "published": "2009-10-30T14:40:31.000Z",
  "updated": "2010-08-30T13:17:05.000Z",
  "title": "Regularity versus singularities for elliptic problems in two dimensions",
  "authors": [
    "Lisa Beck"
  ],
  "comment": "11 pages, revised and slightly extended version",
  "categories": [
    "math.AP"
  ],
  "abstract": "In two dimensions every weak solution to a nonlinear elliptic system $\\rm{div} a(x,u,Du)=0$ has H\\\"older continuous first derivatives provided that standard continuity, ellipticity and growth assumptions hold with a growth exponent $p \\geq 2$. We give an example showing that this result cannot be extended to the subquadratic case, i.e. that weak solutions are not necessarily continuous if $1< p <2$. Furthermore, we discuss related results for variational integrals.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-30T13:17:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J47"
    ],
    "keywords": [
      "elliptic problems",
      "dimensions",
      "regularity",
      "weak solution",
      "singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5876B"
    }
  }
}