{
  "id": "math/0202244",
  "version": "v1",
  "published": "2002-02-23T07:55:03.000Z",
  "updated": "2002-02-23T07:55:03.000Z",
  "title": "Blow-up solutions of nonlinear elliptic equations in R^n with critical exponent",
  "authors": [
    "Man Chun Leung"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "For an integer $n \\ge 3$ and any positive number $\\epsilon$ we establish the existence of smooth functions K on $R^n \\setminus \\{0 \\}$ with $|K - 1| \\le \\epsilon$, such that the equation $\\Delta u + n (n - 2) K u^{{n + 2}\\over {n - 2}} = 0$ in $R^n \\setminus \\{0 \\}$ has a smooth positive solution which blows up at the origin (i.e., u does not have slow decay near the origin). Furthermore, we show that in some cases K can be extended as a Lipschitz function on ${\\R}^n.$ These provide counter-examples to a conjecture of C.-S. Lin when n > 4, and Taliaferro's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-23T07:55:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "53C21"
    ],
    "keywords": [
      "nonlinear elliptic equations",
      "blow-up solutions",
      "critical exponent",
      "lipschitz function",
      "slow decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2244L"
    }
  }
}