A sharp asymptotic remainder estimate for biharmonic Steklov eigenvalues on Riemannian manifolds

2011/04/30 by Genqian Liu, Liu, Genqian
Computer Science · Mathematics · #35P20 #58C40 #58J50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1105.0076

openalex publication_date 2011/04/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let Ω be a bounded domain with C^∞ boundary in an n-dimensional C^∞ Riemannian manifold, and let \varrho be a non-negative bounded function defined on ∂ Ω. It is well-known that for the biharmonic equation Δ² u=0 in Ω with the 0-Dirichlet boundary condition, there exists an infinite set \u_k\ of biharmonic functions in Ω with positive eigenvalues \λ_k\ satisfying Δu_k+ λ_k \varrho (∂ u_k)/(∂ ν)=0 on the boundary ∂ Ω. In this paper, we give the Weyl-type asymptotic formula with a sharp remainder estimate for the counting function of the biharmonic Steklov eigenvalues λ_k.

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