Acta Mathematica Vietnamica
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An Improvement on Discrete Li–Yau Inequality
Bin Shen , Yuhan Zhupp. 75-84
Abstract
In this paper, we study the discrete Li–Yau gradient estimates for the positive solutions u to the heat equation on graphs under $CDE(n,-K)$ condition and derive a sharper estimate than Bauer et al. (J. Differ. Geom. 99(3), 359–405 2015) and Wang and Zhang (Comm. Anal. Geom. 27(4), 969–989 2019).