{
  "id": "math/0601662",
  "version": "v3",
  "published": "2006-01-27T17:32:10.000Z",
  "updated": "2006-06-11T23:19:06.000Z",
  "title": "Lp estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities",
  "authors": [
    "Dimiter Vassilev"
  ],
  "comment": "Corrected some typos and misprints and added a few comments and references to improve presentation. New version of Theorem 2.5 and an additional result on uniqueness/comparison principle for the considered p-laplacian equations",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp $L^q$ regularity for finite energy solutions of p-laplace equations involving critical exponents and possible singularity on a sub-space of $\\mathbb{R}^n$, which imply asymptotic behavior of the solutions at infinity. In addition, we find the best constant and extremals in the case of the considered $L^2$ Hardy-Sobolev inequality.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-06-11T23:19:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J65",
      "35B05"
    ],
    "keywords": [
      "finite energy solutions",
      "hardy-sobolev inequality",
      "lp estimates",
      "hardy-sobolev type inequalities",
      "best constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1662V"
    }
  }
}