{
  "id": "1603.05046",
  "version": "v1",
  "published": "2016-03-16T11:45:05.000Z",
  "updated": "2016-03-16T11:45:05.000Z",
  "title": "On a PDE involving the ${\\cal A}_{p(\\cdot)}$-Laplace operator",
  "authors": [
    "Mihai Mihăilescu",
    "Dušan Repovš"
  ],
  "journal": "Nonlinear Anal. 75:2 (2012), 975-981",
  "doi": "10.1016/j.na.2011.09.034",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper establishes existence of solutions for a partial differential equation in which a differential operator involving variable exponent growth conditions is present. This operator represents a generalization of the $p(\\cdot)$-Laplace operator, i.e. $\\Delta_{p(\\cdot)}u={\\rm div}(|\\nabla u|^{p(\\cdot)-2}\\nabla u)$, where $p(\\cdot)$ is a continuous function. The proof of the main result is based on Schauder's fixed point theorem combined with adequate variational arguments. The function space setting used here makes appeal to the variable exponent Lebesgue and Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-16T11:45:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B38",
      "35J60",
      "35J92"
    ],
    "keywords": [
      "laplace operator",
      "partial differential equation",
      "schauders fixed point theorem",
      "variable exponent growth conditions",
      "paper establishes existence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160305046M"
    }
  }
}