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arXiv · 1811.02263

Some Remarks on the Dirichlet Problem on Infinite Trees

Nikolaos Chalmoukis·Matteo Levi
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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.

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Nikolaos Chalmoukis, Matteo Levi. 2018-11-06. Some Remarks on the Dirichlet Problem on Infinite Trees. https://doi.org/10.1515/conop-2019-0002

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