Backward Harnack inequality and Hamilton estimates for heat type equations
Analysis of PDEs
2025-08-28 v1 Differential Geometry
Abstract
Based on gradient estimates for the heat equation by Hamilton, we discover a backward in time Harnack inequality for positive solutions on compact manifolds without further restrictions such as boundedness or vanishing boundary value for solutions. Contrary to the usual Harnack inequality, it allows comparison of the values of a solution at two different space time points, in both directions of time. In view of the importance of the usual Harnack inequality, further application is expected.
Keywords
Cite
@article{arxiv.2508.19680,
title = {Backward Harnack inequality and Hamilton estimates for heat type equations},
author = {Juanling Lu and Yuting Wu and Qi S. Zhang},
journal= {arXiv preprint arXiv:2508.19680},
year = {2025}
}