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arXiv · 2602.23818

Asymptotic behavior and spectral distortion for biharmonic Steklov problems on thin domains

Bauyrzhan Derbissaly·Pier Domenico Lamberti
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Abstract

In this paper, we investigate the asymptotic behavior of the eigenvalues and eigenfunctions of a biharmonic Steklov problem defined on a thin domain in the $n$ dimensional Euclidean space degenerating to a segment. For $n=2$ the problem models the vibrations of a thin elastic plate with cross section represented by the given domain and mass concentrated on a free boundary. The problem under consideration depends on a parameter $\sigma$ that in the theory of elastic plates represents the Poisson ratio of the material. Our analysis points out a distortion in the limiting problem depending on $\sigma$ and the space dimension $n$.

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Bauyrzhan Derbissaly, Pier Domenico Lamberti. 2026-02-27. Asymptotic behavior and spectral distortion for biharmonic Steklov problems on thin domains. https://arxiv.org/abs/2602.23818

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