{
  "id": "0912.3048",
  "version": "v2",
  "published": "2009-12-16T03:30:18.000Z",
  "updated": "2010-07-08T17:49:28.000Z",
  "title": "Hardy-Sobolev Type Equations for p-Laplacian, 1 < p < 2, in Bounded Domain",
  "authors": [
    "M. Bhakta",
    "A. Biswas"
  ],
  "comment": "27 pages",
  "journal": "Differential and Integral Equations, Vol. 24, N0. 1-2, 2011",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study quasilinear degenerate singular elliptic equation of type -Delta_p u = \\frac{u^{p^*(s)-1}}{|y|^t}$ in a smooth bounded domain \\Omega in R^n=R^k \\times R^{N-k}$, x=(y,z) in R^k \\times R^{N-k}, 2 \\leq k<N and N \\geq 3, 1<p<2, 0\\leq s\\leq p, 0\\leq t\\leq s, p^*(s)=\\frac{p(n-s)}{n-p}. We study existence of solution for t<s, non-existence in a star-shaped domain for t=s and s<k(\\frac{p-1}{p}). We also show that solution is in C^{1,\\al}(\\Omega) for some 0<\\al<1 provided t<\\frac{k}{N}(\\frac{p-1}{p}). The regularity of solution can be improved to the class W^{2,p}(\\Omega) when t<k(\\frac{p-1}{p}). We also study some properties of the singular sets in a cylindrically symmetric domain using the method of symmetry.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-08T17:49:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J70",
      "35J75",
      "35B09",
      "35B65"
    ],
    "keywords": [
      "hardy-sobolev type equations",
      "bounded domain",
      "study quasilinear degenerate singular elliptic",
      "quasilinear degenerate singular elliptic equation",
      "p-laplacian"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3048B"
    }
  }
}