English

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 \mG\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\mG.

Keywords

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}
}