Steklov Eigenvalue Problem on Subgraphs of Integer Lattices

2019/02/15 by Wen Han, Bobo Hua, Han, Wen +1 · 4 citations
Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1902.05831

openalex publication_date 2019/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the eigenvalues of the Dirichlet-to-Neumann operator on a finite subgraph of the integer lattice Zn. We estimate the first n+1 eigenvalues using the number of vertices of the subgraph. As a corollary, we prove that the first non-trivial eigenvalue of the Dirichlet-to-Neumann operator tends to zero as the number of vertices of the subgraph tends to infinity.

Citations

• Cheeger estimates of Dirichlet-to-Neumann operators on infinite subgraphs of graphs

Cited by

• The first Steklov eigenvalue bound for graphs of positive genus
• Higher Steklov eigenvalues of graphs on surfaces
• A generalized Cheeger inequality and the Steklov Problem on finite graphs
• Comparison between the first Steklov eigenvalue and algebraic connectivity on trees

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• Cheeger estimates of Dirichlet-to-Neumann operators on infinite subgraphs of graphs
• Upper bounds for the Steklov eigenvalues on trees