A note on Neumann problems on graphs
Analysis of PDEs
2018-03-26 v1
Abstract
We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.
Cite
@article{arxiv.1803.08559,
title = {A note on Neumann problems on graphs},
author = {Michael Hinz and Michael Schwarz},
journal= {arXiv preprint arXiv:1803.08559},
year = {2018}
}