{
  "id": "math/0408238",
  "version": "v1",
  "published": "2004-08-18T09:53:06.000Z",
  "updated": "2004-08-18T09:53:06.000Z",
  "title": "On a Yamabe Type Problem on Three Dimensional Thin Annulus",
  "authors": [
    "Mohamed Ben Ayed",
    "Khalil El Mehdi",
    "Mokhless Hammami",
    "Mohameden Ould Ahmedou"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a Yamabe type problem on a family $A_\\epsilon$ of annulus shaped domains of $\\R^3$ which becomes \"thin\" as $\\epsilon$ goes to zero. We show that, for any given positive constant $C$, there exists $\\epsilon_0$ such that for any $\\epsilon < \\epsilon_0$, the problem has no solution $u_\\epsilon$ whose energy is less than $C$. Such a result extends to dimension three a result previously known in higher dimensions. Although the strategy to prove this result is the same as in higher dimensions, we need a more careful and delicate blow up analysis of asymptotic profiles of solutions $u_\\epsilon$ when $\\epsilon$ goes to zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-18T09:53:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J65",
      "58E05",
      "35B40"
    ],
    "keywords": [
      "yamabe type problem",
      "dimensional thin annulus",
      "higher dimensions",
      "result extends",
      "asymptotic profiles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8238B"
    }
  }
}