Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics

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Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 34
2001-03 発行

A Weighted Sobolev-Poincare's Inequality on Infinite Networks

Murakami, Atsushi
Yamasaki, Maretsugu
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Description
Inequalities on networks have played important roles in the theory of networks. We study the famous Sobolev-Poincare's inequality on infinite net-works in the weighted form. This inequality is closely related to the smallest eigenvalue of a weighted discrete Laplacian. We give a dual characterization for the smallest eigenvalue.