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On shape optimization for fourth order Steklov eigenvalue problems

2024/10/28 by Changwei Xiong, Xiong, Changwei, J. S. Yu +2
Engineering · #Advanced Numerical Analysis Techniques #Elasticity and Wave Propagation #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2410.20805

Abstract

We study three types of fourth-order Steklov eigenvalue problems. For the first two of them, we derive the asymptotic expansion of their spectra on Euclidean annular domains \mathbbBn1∖ \mathbbBnε as ε→ 0, leading to conclusions on shape optimization. For these two problems, we also compute their spectra on cylinders over closed Riemannian manifolds. Last, for the third problem, we obtain a sharp upper bound for its first non-zero eigenvalue on star-shaped and mean convex Euclidean domains.

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