{
  "id": "math/0703873",
  "version": "v1",
  "published": "2007-03-29T08:31:08.000Z",
  "updated": "2007-03-29T08:31:08.000Z",
  "title": "A weighted Moser-Trudinger inequality and its relation to the Caffarelli-Kohn-Nirenberg inequalities in two space dimensions",
  "authors": [
    "Jean Dolbeault",
    "Maria J. Esteban",
    "Gabriella Tarantello"
  ],
  "journal": "Annali della Scuola Normale Superiore di Pisa 7 (2008) 313-341",
  "categories": [
    "math.AP"
  ],
  "abstract": "We first prove a weighted inequality of Moser-Trudinger type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than -1. Without symmetry assumption, it holds if and only if the parameter is in the interval (-1,0]. The inequality gives us some insight on the symmetry breaking phenomenon for the extremal functions of the Hardy-Sobolev inequality, as established by Caffarelli-Kohn-Nirenberg, in two space dimensions. In fact, for suitable sets of parameters (asymptotically sharp) we prove symmetry or symmetry breaking by means of a blow-up method. In this way, the weighted Moser-Trudinger inequality appears as a limit case of the Hardy-Sobolev inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-29T08:31:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "46E35",
      "58E35"
    ],
    "keywords": [
      "space dimensions",
      "caffarelli-kohn-nirenberg inequalities",
      "hardy-sobolev inequality",
      "two-dimensional euclidean space",
      "weighted moser-trudinger inequality appears"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3873D"
    }
  }
}