Hokkaido Mathematical Journal

Hokkaido Mathematical Journal, 37 (2008) pp.59-73

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Abstract

In the context of an infinite network $N$, the Dirichlet problem with respect to an arbitrary subset of vertices $N$ is solved.Using this solution, some of the important potential-theoretic concepts like Balayage, Domination principle, and Poisson kernel are investigated in $N$.

MSC(Primary) 31B15(MSC2000), 31C12(MSC2000) infinite network, Dirichlet problem, Poisson kernel, Balayage, Green's formulas