Li-Yau inequality and related properties on metric star graphs
Analysis of PDEs
2025-01-23 v1
Abstract
We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph 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 .
Cite
@article{arxiv.2501.12685,
title = {Li-Yau inequality and related properties on metric star graphs},
author = {Fabio Camilli},
journal= {arXiv preprint arXiv:2501.12685},
year = {2025}
}