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arXiv · 1112.1206

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

Genqian Liu
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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.

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Genqian Liu. 2012-04-02. Sharp Weyl-Type Formulas of the Spectral Functions for Biharmonic Steklov Eigenvalues. https://arxiv.org/abs/1112.1206

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