{
  "id": "0912.3994",
  "version": "v3",
  "published": "2009-12-20T08:19:47.000Z",
  "updated": "2011-01-31T09:50:22.000Z",
  "title": "The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds",
  "authors": [
    "Genqian Liu"
  ],
  "comment": "42 pages",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "Let $\\Omega$ be a bounded domain with $C^2$-smooth boundary in an $n$-dimensional oriented Riemannian manifold. It is well-known that for the bi-harmonic 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, by a new method we establish the Weyl-type asymptotic formula for the counting function of the biharmonic Stekloff eigenvalues $\\lambda_k$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-31T09:50:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P20",
      "58C40",
      "58J50"
    ],
    "keywords": [
      "dirichlet boundary condition",
      "weyl-type asymptotic formula",
      "biharmonic steklov eigenvalues",
      "biharmonic stekloff eigenvalues",
      "dimensional oriented riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3994L"
    }
  }
}