English

Some Remarks on the Dirichlet Problem on Infinite Trees

Classical Analysis and ODEs 2023-04-18 v1 Combinatorics

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 W1,p W^{1,p} of the tree.

Keywords

Cite

@article{arxiv.1811.02263,
  title  = {Some Remarks on the Dirichlet Problem on Infinite Trees},
  author = {Nikolaos Chalmoukis and Matteo Levi},
  journal= {arXiv preprint arXiv:1811.02263},
  year   = {2023}
}

Comments

14 pages, 1 figure

R2 v1 2026-06-23T05:05:55.964Z