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 48
2015-03 発行

1-harmonic functions on a network

倉田 久靖
山﨑 稀嗣
ファイル
内容記述(抄録等)
A minimizer of the Dirichlet norm of order 1 is called a 1-harmonic function. The aim of this paper is a research of properties of 1-harmonic functions on a network. First we consider the 1-Dirichlet space and show that every network is of 1-hyperbolic type and that the ideal boundary coincides with the 1-harmonic boundary. Next we introduce the notion of 1-harmonic functions and that of strongly 1-harmonic functions. We discuss the Dirichlet problem and the maximum principle with respect to (strongly) 1-harmonic functions.