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Li-Yau Inequality and Related Properties on Metric Star Graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月3日

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  • Fabio Camilli

摘要

We prove a Li-Yau gradient estimate for positive solutions to the heat equation defined on a metric star graph \(\mathcal {G}\) 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 \(\mathcal {G}\) G .