We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph G 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 G.
Li-Yau Inequality and Related Properties on Metric Star Graphs
Camilli F.
2025-01-01
Abstract
We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph G 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 G.File in questo prodotto:
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