{
  "id": "1108.2947",
  "version": "v2",
  "published": "2011-08-15T07:14:29.000Z",
  "updated": "2012-01-18T12:15:23.000Z",
  "title": "Partial regularity of $p(x)$-harmonic maps",
  "authors": [
    "Maria Alessandra Ragusa",
    "Atsushi Tachikawa",
    "Hiroshi Takabayashi"
  ],
  "comment": "This paper has been withdraw by the author. Because it has been accepted, and the copyright assign to the publisher",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $(g^{\\alpha\\beta}(x))$ and $(h_{ij}(u))$ be uniformly elliptic symmetric matrices, and assume that $h_{ij}(u)$ and $p(x) \\, (\\, \\geq 2)$ are sufficiently smooth. We prove partial regularity of minimizers for the functional [ {\\mathcal F}(u) = \\int_\\Omega (g^{\\alpha \\beta}(x) h_{ij}(u) D_\\alpha u^iD_\\beta u^j)^{p(x)/2} dx, \\] under the non-standard growth conditions of $p(x)$-type. If $g^{\\alpha\\beta}(x)$ are in the class $VMO$, we have partial H\\\"older regularity. Moreover, if $g^{\\alpha\\beta}$ are H\\\"older continuous, we can show partial $C^{1,\\alpha}$-regularity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-18T12:15:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J47",
      "35J60",
      "49N60",
      "58E20"
    ],
    "keywords": [
      "partial regularity",
      "harmonic maps",
      "uniformly elliptic symmetric matrices",
      "non-standard growth conditions",
      "sufficiently smooth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2947A"
    }
  }
}