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arXiv · 1901.00637

Discrete harmonic functions in Lipschitz domains

Sami Mustapha·Mohamed Sifi
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Abstract

We prove the existence and uniqueness of a discrete nonnegative harmonic function for a random walk satisfying finite range, centering and ellipticity conditions, killed when leaving a globally Lipschitz domain in $\mathbb{Z}^d$. Our method is based on a systematic use of comparison arguments and discrete potential-theoretical techniques.

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Sami Mustapha, Mohamed Sifi. 2019-01-03. Discrete harmonic functions in Lipschitz domains. https://arxiv.org/abs/1901.00637

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