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arXiv · 2410.20805

On shape optimization for fourth order Steklov eigenvalue problems

Changwei Xiong·Jinglong Yang·Jinchao Yu
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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 $\mathbb{B}^n_1\setminus \overline{\mathbb{B}^n_\epsilon}$ as $\epsilon \to 0$, 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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Changwei Xiong, Jinglong Yang, Jinchao Yu. 2024-10-28. On shape optimization for fourth order Steklov eigenvalue problems. https://arxiv.org/abs/2410.20805

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