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arXiv · 2203.12530

Poincar\'e inequalities on graphs

Matteo Levi·Federico Santagati·Anita Tabacco·Maria Vallarino
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Abstract

We prove local $L^p$-Poincar\'e inequalities, $ p\in[1,\infty]$, on quasiconvex sets in infinite graphs endowed with a family of locally doubling measures, and global $L^p$-Poincar\'e inequalities on connected sets for flow measures on trees. We also discuss the optimality of our results.

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Matteo Levi, Federico Santagati, Anita Tabacco, Maria Vallarino. 2022-03-23. Poincar\'e inequalities on graphs. https://doi.org/10.1007/s10476-023-0215-5

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