{
  "id": "1112.1206",
  "version": "v2",
  "published": "2011-12-06T09:41:00.000Z",
  "updated": "2012-04-02T09:04:40.000Z",
  "title": "Sharp Weyl-Type Formulas of the Spectral Functions for Biharmonic Steklov Eigenvalues",
  "authors": [
    "Genqian Liu"
  ],
  "comment": "24 pages. arXiv admin note: substantial text overlap with arXiv:1105.0076",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, by explicitly calculating the principal symbols of pseudodifferential operators and by applying H\\\"omander's spectral function theorem, we obtain the Weyl-type asymptotic formulas with sharp remainder estimates for the counting functions of the two classes of biharmonic Steklov eigenvalues $\\lambda_k$ and $\\mu_k$ in a smooth bounded domain of a Riemannian manifold. This solves a longstanding challenging problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-02T09:04:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P20",
      "58C40",
      "58J50"
    ],
    "keywords": [
      "biharmonic steklov eigenvalues",
      "sharp weyl-type formulas",
      "spectral function theorem",
      "sharp remainder estimates",
      "weyl-type asymptotic formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1206L"
    }
  }
}