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Monotonicity of Steklov eigenvalues on graphs and applications

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Abstract

In this paper, we obtain monotonicity of Steklov eigenvalues on graphs which as a special case on trees extends the results of He and Hua (Steklov flows on trees and applications. arXiv:2103.07696) to higher Steklov eigenvalues and gives affirmative answers to two problems proposed in He and Hua (arXiv:2103.07696). As applications of the monotonicity of Steklov eigenvalues, we obtain some estimates for Steklov eigenvalues on trees generalizing the isodiametric estimate for the first positive Steklov eigenvalues on trees in He and Hua (Calc Var Partial Differ Equ 61(3):101, 2022. arXiv:2011.11014).

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, Guangdong, China

    Chengjie Yu & Yingtao Yu

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  1. Chengjie Yu
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  2. Yingtao Yu
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Correspondence to Chengjie Yu.

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Communicated by F.-H. Lin.

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Research partially supported by GDNSF with contract no. 2021A1515010264 and NNSF of China with contract no. 11571215.

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Yu, C., Yu, Y. Monotonicity of Steklov eigenvalues on graphs and applications. Calc. Var. 63, 79 (2024). https://doi.org/10.1007/s00526-024-02683-y

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