{
  "id": "1105.0076",
  "version": "v2",
  "published": "2011-04-30T11:55:02.000Z",
  "updated": "2012-01-01T06:42:42.000Z",
  "title": "A sharp asymptotic remainder estimate for biharmonic Steklov eigenvalues on Riemannian manifolds",
  "authors": [
    "Genqian Liu"
  ],
  "comment": "This paper has been withdrawn by the author",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Let $\\Omega$ be a bounded domain with $C^\\infty$ boundary in an $n$-dimensional $C^\\infty$ Riemannian manifold, and let $\\varrho$ be a non-negative bounded function defined on $\\partial \\Omega$. It is well-known that for the biharmonic equation $\\Delta^2 u=0$ in $\\Omega$ with the 0-Dirichlet boundary condition, there exists an infinite set $\\{u_k\\}$ of biharmonic functions in $\\Omega$ with positive eigenvalues $\\{\\lambda_k\\}$ satisfying $\\Delta u_k+ \\lambda_k \\varrho \\frac{\\partial u_k}{\\partial \\nu}=0$ on the boundary $\\partial \\Omega$. In this paper, we give the Weyl-type asymptotic formula with a sharp remainder estimate for the counting function of the biharmonic Steklov eigenvalues $\\lambda_k$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-01T06:42:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P20",
      "58C40",
      "58J50"
    ],
    "keywords": [
      "sharp asymptotic remainder estimate",
      "biharmonic steklov eigenvalues",
      "riemannian manifold",
      "sharp remainder estimate",
      "weyl-type asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.0076L"
    }
  }
}