Discrete versions of the Li-Yau gradient estimate

2017/01/17 by Dier, Dominik, Kassmann, Moritz, Zacher, Rico
#05C10 #05C81 #35K05 #35K10 #35R02 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.04807

Abstract

We study positive solutions to the heat equation on graphs. We prove variants of the Li-Yau gradient estimate and the differential Harnack inequality. For some graphs, we can show the estimates to be sharp. We establish new computation rules for differential operators on discrete spaces and introduce a relaxation function that governs the time dependency in the differential Harnack estimate.

Related

• Remarks on Li-Yau inequality on graphs
• A gradient estimate for positive functions on graphs
• Global gradient estimate on graph and its applications
• Li-Yau inequality and related properties on metric star graphs
• Li-Yau Type Gradient Estimates and Harnack Inequalities by Stochastic Analysis