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Sharp bounds for higher mixed Steklov-Robin eigenvalues on domains with holes
Abstract
This article is concerned with mixed Steklov--Robin eigenvalues on bounded domains in ℝn, n ≥ 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 ∈ {2, 3, …, 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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BibTeX
@misc{basak2026sharp,
title = {{Sharp bounds for higher mixed Steklov-Robin eigenvalues on domains with holes}},
author = {Sagar Basak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21326},
eprint = {2609.21326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21326},
}
RIS
TY - UNPB
TI - Sharp bounds for higher mixed Steklov-Robin eigenvalues on domains with holes
AU - Sagar Basak
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21326
UR - https://arxiv.org/abs/2609.21326
AB - This article is concerned with mixed Steklov--Robin eigenvalues on bounded domains in ℝ^n, n ≥ 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 ∈ {2, 3, …, n+1}. We provide examples to emphasize the fact that the symmetry assumptions, on the family of domains considered, are crucial.
ER -