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

2011/12/06 by Liu, Genqian
#35P20 #58C40 #58J50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1112.1206

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 λ_k and μ_k in a smooth bounded domain of a Riemannian manifold. This solves a longstanding challenging problem.

Related

• The Weyl-type asymptotic formula for biharmonic Stekloff eigenvalues with Neumann boundary condition in Riemannian manifolds
• The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds
• A sharp asymptotic remainder estimate for biharmonic Steklov eigenvalues on Riemannian manifolds
• Upper bound of the counting function of Steklov eigenvalues
• Biharmonic Steklov operator on differential forms