Dirichlet problems on graphs with ends

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:420

Article

Perkins, Tony L.

关键词: Discrete;    Subharmonic;    Potential theory;    Dirichlet problem;   

DOI  :  10.1016/j.jmaa.2014.06.064

来源: Elsevier

【 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.

【 授权许可】

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