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島根大学理学部紀要 26 巻
1992-12-25 発行
無限ネットワーク上の非線形ポテンシャル
Nonlinear Potentials on an Infinite Network
村上 温
山﨑 稀嗣
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The aim of this paper is to study some properties, of Dirichlet potentials and pure potentials of order p on an infinite network. It will be shown that several assumptions in the theory of general nonlinear potential theory are fulfilled in our case. The space of Dirichlet potentials of order p will play a crucial role in our study if the network is hyperbolic of order p. A nonlinear version of Cartan's domination principle will be shown with elementary properties of p-superharmonic functions.
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