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First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs

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Abstract

Following Escobar (J Funct Anal 150(2):544–556, 1997) and Jammes (Ann l’Inst Fourier 65(3):1381–1385, 2015), we introduce two types of isoperimetric constants and give lower bound estimates for the first nontrivial eigenvalues of Dirichlet-to-Neumann operators on finite graphs with boundary respectively.

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Acknowledgements

We would like to thank the anonymous referee for his/her helpful comments and suggestions.

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Correspondence to Yan Huang.

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Communicated by J. Jost.

Bobo Hua is supported in part by NSFC, No. 11401106. Zuoqin Wang is supported in part by NSFC, Nos. 11571131 and 11526212.

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Hua, B., Huang, Y. & Wang, Z. First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs. Calc. Var. 56, 178 (2017). https://doi.org/10.1007/s00526-017-1260-3

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