{
  "id": "1312.6286",
  "version": "v1",
  "published": "2013-12-21T18:26:29.000Z",
  "updated": "2013-12-21T18:26:29.000Z",
  "title": "Description of the lack of compactness in Orlicz spaces and applications",
  "authors": [
    "Ines Ben Ayed",
    "Mohamed Khalil Zghal"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1003.2562, arXiv:1302.1269 by other authors",
  "categories": [
    "math.AP",
    "math.CA",
    "math.FA"
  ],
  "abstract": "In this paper, we investigate the lack of compactness of the Sobolev embedding of $H^1(\\R^2)$ into the Orlicz space $L^{{\\phi}_p}(\\R^2)$ associated to the function $\\phi_p$ defined by $\\phi_p(s):={\\rm{e}^{s^2}}-\\Sum_{k=0}^{p-1} \\frac{s^{2k}}{k!}\\cdot$ We also undertake the study of a nonlinear wave equation with exponential growth where the Orlicz norm $\\|.\\|_{L^{\\phi_p}}$ plays a crucial role. This study includes issues of global existence, scattering and qualitative study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-21T18:26:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orlicz space",
      "compactness",
      "description",
      "applications",
      "nonlinear wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6286B"
    }
  }
}