Dirichlet problems on graphs with ends

作者：Perkins Tony L^*

来源：Journal of Mathematical Analysis and Applications, 2014, 420(2): 1182-1194.

DOI：10.1016/j.jmaa.2014.06.064

• Discrete
• Subharmonic
• Potential theory
• Dirichlet problem

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.

• 出版日期2014-12-15