A note on Li-Yau type gradient estimate
Chengjie Yu, Feifei Zhao
TL;DR
This paper develops new Li-Yau type gradient estimates with time-dependent parameters for the heat equation, improving upon previous estimates by Li-Xu and Qian, and enhances Davies' classical results.
Contribution
It introduces novel Li-Yau type gradient estimates with time-dependent parameters, distinct from prior work, and applies these to improve existing gradient bounds.
Findings
New gradient estimates with time-dependent parameters
Improved bounds on positive solutions of the heat equation
Enhanced classical Li-Yau gradient estimates
Abstract
In this paper, we obtain Li-Yau type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu \cite{LX} and Qian \cite{Qi}. As an application of the estimate, we also obtained improvements of Davies' Li-Yau type gradient estimate.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Numerical methods in inverse problems