{
  "id": "1206.4341",
  "version": "v2",
  "published": "2012-06-19T21:10:32.000Z",
  "updated": "2013-01-22T09:30:57.000Z",
  "title": "On the pure critical exponent problem for the $p$-Laplacian",
  "authors": [
    "Carlo Mercuri",
    "Filomena Pacella"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove existence and multiplicity of positive and sign-changing solutions to the pure critical exponent problem for the $p$-Laplacian operator with Dirichlet boundary conditions on a bounded domain having nontrivial topology and discrete symmetry. Pioneering works related to the case $p=2$ are H. Brezis and L. Nirenberg [4], J.-M. Coron [10], and A. Bahri and J.-M. Coron [3]. A global compactness analysis is given for the Palais-Smale sequences in the presence of symmetries.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-01-22T09:30:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J66",
      "35J92"
    ],
    "keywords": [
      "pure critical exponent problem",
      "dirichlet boundary conditions",
      "global compactness analysis",
      "palais-smale sequences",
      "nontrivial topology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.4341M"
    }
  }
}