Sharp Weyl-Type Formulas of the Spectral Functions for Biharmonic Steklov Eigenvalues

Abstract

In this paper, by explicitly calculating the principal symbols of pseudodifferential operators and by applying Hömander'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.

24 pages. arXiv admin note: substantial text overlap with arXiv:1105.0076

References in corpus (1)

• Spectral Theory for Perturbed Krein Laplacians in Nonsmooth Domains