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arXiv · 1803.08559

A note on Neumann problems on graphs

Michael Hinz·Michael Schwarz
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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.

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Michael Hinz, Michael Schwarz. 2018-03-22. A note on Neumann problems on graphs. https://arxiv.org/abs/1803.08559

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