Li-Yau inequality and related properties on metric star graphs

2025/01/22 by Fabio Camilli, Camilli, Fabio
Computer Science · Mathematics · #35A23 #35R02 #58J35 #Advanced Graph Theory Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2501.12685

openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph \mG given by the heat kernel formula. As consequence, we derive a Harnack estimate and a Liouville property for bounded harmonic functions. The argument exploits an explicit representation formula for the heat kernel on \mG.

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