Some remarks on the Dirichlet problem on infinite trees

Abstract

We consider the Dirichlet problem on in_nite and locally _nite rooted trees, andwe prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev W1,p of the tree.

Keywords

• potential theory
• discrete dirichlet problem
• boundary values and capacities
• primary: 31c15. secondary: 05c63
• 05c05