An Improved Harnack Inequality for Dirichlet Eigenvalues of Abelian Homogeneous Graphs
Received:October 16, 2013  Revised:June 18, 2014
Key Words: Laplace operator   Harnack inequality   eigenvalue estimate.  
Fund Project:Partially supported by National Natural Science Foundation of China (Grant No.11271011).
Author NameAffiliation
Shoudong MAN Department of Mathematics, School of Information, Renmin University of China, Beijing 100872, P. R. China 
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Abstract:
      In this paper, we prove an improved Harnack inequality for Dirichlet eigenfunctions of abelian homogeneous graphs and their convex subgraphs. As a consequence, we derive a lower estimate for Dirichlet eigenvalues using the Harnack inequality, extending previous results of Chung and Yau for certain homogeneous graphs.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.06.002
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