{
  "id": "1310.4435",
  "version": "v1",
  "published": "2013-10-16T16:20:26.000Z",
  "updated": "2013-10-16T16:20:26.000Z",
  "title": "Regularity of minimizers of autonomous convex variational integrals",
  "authors": [
    "Menita Carozza",
    "Jan Kristensen",
    "Antonia Passarelli di Napoli"
  ],
  "doi": "10.2422/2036-2145.201208_005",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish local higher integrability and differentiability results for minimizers of variational integrals $$ \\mathfrak{F}(v,\\Omega) = \\int_{\\Omega} /! F(Dv(x)) \\, dx $$ over $W^{1,p}$--Sobolev mappings $u \\colon \\Omega \\subset {\\mathbb R}^n \\to {\\mathbb R}^N$ satisfying a Dirichlet boundary condition. The integrands $F$ are assumed to be autonomous, convex and of $(p,q)$ growth, but are otherwise not subjected to any further structure conditions, and we consider exponents in the range $1<p \\leq q < p^{\\ast}$, where $p^{\\ast}$ denotes the Sobolev conjugate exponent of $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-16T16:20:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N15",
      "49N60",
      "49N99"
    ],
    "keywords": [
      "autonomous convex variational integrals",
      "minimizers",
      "regularity",
      "establish local higher integrability",
      "sobolev conjugate exponent"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4435C"
    }
  }
}