On the Li-Yau type gradient estimate of Li and Xu
Zhigang Chen, Chengjie Yu, Feifei Zhao
TL;DR
This paper develops a new Li-Yau type gradient estimate for the heat equation with time-dependent parameters, generalizing previous results and improving upon Davies' estimates through a novel approach.
Contribution
It introduces a generalized Li-Yau gradient estimate with time-dependent parameters, encompassing Li-Xu's estimates as special cases and offering improvements over Davies' results.
Findings
Derived a new gradient estimate with time-dependent parameters
Unified previous Li-Xu estimates within a broader framework
Enhanced the bounds of Davies' Li-Yau type estimates
Abstract
In this paper, we obtain a Li-Yau type gradient estimate with time dependent parameter for positive solutions of the heat equation, so that the Li-Yau type gradient estimate of Li-Xu are special cases of the estimate. We also obtain improvements of Davies' Li-Yau type gradient estimate. The argument is different with those of Li-Xu and Qian.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Numerical methods in inverse problems