Steklov Eigenvalue Problem on Subgraphs of Integer Lattices
Spectral Theory
2020-09-15 v3
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.
Keywords
Cite
@article{arxiv.1902.05831,
title = {Steklov Eigenvalue Problem on Subgraphs of Integer Lattices},
author = {Wen Han and Bobo Hua},
journal= {arXiv preprint arXiv:1902.05831},
year = {2020}
}
Comments
This is a revision of the paper