Dirichlet problems on graphs with ends

被引:0
作者
Perkins, Tony L. [1 ]
机构
[1] Spring Hill Coll, Dept Math, Mobile, AL 36608 USA
关键词
Discrete; Subharmonic; Potential theory; Dirichlet problem;
D O I
10.1016/j.jmaa.2014.06.064
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In classical potential theory, one can solve the Dirichlet problem on unbounded domains such as the upper half plane. These domains have two types of boundary points; the usual finite boundary points and another point at infinity. W. Woess has solved a discrete version of the Dirichlet problem on the ends of graphs analogous to having multiple points at infinity and no finite boundary. Whereas C. Kiselman has solved a similar version of the Dirichlet problem on graphs analogous to bounded domains. In this work, we combine the two ideas to solve a version of the Dirichlet problem on graphs with finitely many ends and boundary points of the Kiselman type. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:1182 / 1194
页数:13
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