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.
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Fund Project:Partially supported by National Natural Science Foundation of China (Grant No.11271011). |
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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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