島根大学総合理工学部紀要.シリーズB

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島根大学総合理工学部紀要.シリーズB 34
2001-03 発行

A Weighted Sobolev-Poincare's Inequality on Infinite Networks

村上 温
山﨑 稀嗣
ファイル
内容記述(抄録等)
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.