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arXiv:1112.1206 [math.AP]AbstractReferencesReviewsResources

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

Genqian Liu

Published 2011-12-06, updated 2012-04-02Version 2

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.

Comments: 24 pages. arXiv admin note: substantial text overlap with arXiv:1105.0076
Categories: math.AP
Subjects: 35P20, 58C40, 58J50
Related articles:
arXiv:1105.0076 [math.AP] (Published 2011-04-30, updated 2012-01-01)
A sharp asymptotic remainder estimate for biharmonic Steklov eigenvalues on Riemannian manifolds
arXiv:0912.3994 [math.AP] (Published 2009-12-20, updated 2011-01-31)
The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds

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