{
  "id": "0810.4134",
  "version": "v8",
  "published": "2008-10-22T19:09:15.000Z",
  "updated": "2009-07-03T10:08:29.000Z",
  "title": "The Best Constant, the Nonexistence of Extremal Functions and Related Results for an Improved Hardy-Sobolev Inequality",
  "authors": [
    "N. B. Zographopoulos"
  ],
  "comment": "12pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We present the best constant and the existence of extremal functions for an Improved Hardy-Sobolev inequality. We prove that, under a proper transformation, this inequality is equivalent to the Sobolev inequality in $\\mathbb{R}^N$. We also discuss the connection of the related functional spaces and as a result we obtain some Caffarelli - Kohn - Nirenberg inequalities. Our starting point is the existence of a minimizer for the Bliss' inequality and the indirect dependence of the Hardy inequality at the origin.",
  "revisions": [
    {
      "version": "v8",
      "updated": "2009-07-03T10:08:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extremal functions",
      "best constant",
      "hardy-sobolev inequality",
      "related results",
      "nonexistence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.4134Z"
    }
  }
}