{
  "id": "1107.4586",
  "version": "v1",
  "published": "2011-07-22T17:47:14.000Z",
  "updated": "2011-07-22T17:47:14.000Z",
  "title": "Isolated Singularities of Nonlinear Polyharmonic Inequalities",
  "authors": [
    "Steven D. Taliaferro"
  ],
  "comment": "31 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain results for the following question where $m\\ge 1$ and $n\\ge 2$ are integers. {\\bf Question.} For which continuous functions $f\\colon [0,\\infty)\\to [0,\\infty)$ does there exist a continuous function $\\phi\\colon (0,1)\\to (0,\\infty)$ such that every $C^{2m}$ nonnegative solution $u(x)$ of 0 \\le -\\Delta^m u\\le f(u)\\quad \\text{in}\\quad B_2(0)\\backslash\\{0\\}\\subset {\\bb R}^n satisfies u(x) = O(\\phi(|x|))\\quad \\text{as}\\quad x\\to 0 and what is the optimal such $\\phi$ when one exists?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-22T17:47:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B09",
      "35B33",
      "35B40",
      "35B44",
      "35B45",
      "35R45",
      "35J30",
      "35J91"
    ],
    "keywords": [
      "nonlinear polyharmonic inequalities",
      "isolated singularities",
      "continuous function",
      "nonnegative solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.4586T"
    }
  }
}