Some Remarks on the Dirichlet Problem on Infinite Trees

Abstract

We consider the Dirichlet problem on infinite and locally finite rooted trees, and we prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev $W^{1,p}$ of the tree.

14 pages, 1 figure

References in corpus (2)

• The characterization of the Carleson measures for analytic Besov spaces: a simple proof
• Equilibrium measures on trees

Cited by in corpus (4)

• Riesz transform for a flow Laplacian on homogeneous trees
• Analysis on trees with nondoubling flow measures
• Riesz capacities of a set due to Dobiński
• Equilibrium measures on trees