Memoirs of the Faculty of Science, Shimane University

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Memoirs of the Faculty of Science, Shimane University 26
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
Murakami, Atsushi
Yamasaki, Maretsugu
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Description
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.