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arXiv · 2609.21326

Sharp bounds for higher mixed Steklov-Robin eigenvalues on domains with holes

Sagar Basak
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Abstract

This article is concerned with mixed Steklov--Robin eigenvalues on bounded domains in $\mathbb{R}^{n}, n \geq 2$, with Lipschitz boundary. Specifically, we consider domains with symmetry of order $4$ containing a spherical hole. We obtain isoperimetric inequalities for the $k$-th Steklov-Robin eigenvalues for each $k \in \{2, 3, \dots, n+1\}$. We provide examples to emphasize the fact that the symmetry assumptions, on the family of domains considered, are crucial.

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Sagar Basak. 2026-09-18. Sharp bounds for higher mixed Steklov-Robin eigenvalues on domains with holes. https://arxiv.org/abs/2609.21326

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