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arXiv · 0912.3994

The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds

Genqian Liu
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Abstract

Let $Ω$ be a bounded domain with $C^2$-smooth boundary in an $n$-dimensional oriented Riemannian manifold. It is well-known that for the bi-harmonic equation $Δ^2 u=0$ 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 $Δu_k+ λ_k \varrho \frac{\partial u_k}{\partial ν}=0$ on the boundary $\partial Ω$. In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of the biharmonic Stekloff eigenvalues $λ_k$.

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Genqian Liu. 2011-01-31. The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds. https://arxiv.org/abs/0912.3994

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