{
  "id": "1312.5570",
  "version": "v1",
  "published": "2013-12-19T14:52:16.000Z",
  "updated": "2013-12-19T14:52:16.000Z",
  "title": "Global gradient estimates for the $p(\\cdot)$-Laplacian",
  "authors": [
    "Lars Diening",
    "Sebastian Schwarzacher"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider Calder\\'on-Zygmund type estimates for the non-homogeneous $p(\\cdot)$-Laplacian system $ -\\text{div}(|D u|^{p(\\cdot)-2} Du) = -\\text{div}(|G|^{p(\\cdot)-2} G),$ where $p$ is a variable exponent. We show that $|G|^{p(\\cdot)} \\in L^q(\\mathbb{R}^n)$ implies $|D u|^{p(\\cdot)} \\in L^q(\\mathbb{R}^n)$ for any $q \\geq 1$. We also prove local estimates independent of the size of the domain and introduce new techniques to variable analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-19T14:52:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35B65",
      "35B45",
      "35Q35"
    ],
    "keywords": [
      "global gradient estimates",
      "calderon-zygmund type estimates",
      "local estimates independent",
      "laplacian system",
      "variable exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5570D"
    }
  }
}