Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula
Analysis of PDEs
2025-06-16 v1 Differential Geometry
Abstract
In this paper, we establish a new global Hessian matrix estimate for heat-type equations on Riemannian manifolds using a Bismut-type Hessian formula. Our results feature fully explicit coefficients as well as delay / growth rate functions. These estimates yield two key applications: a novel backward weak Harnack inequality and a precise pointwise Hessian estimate for eigenfunctions.
Keywords
Cite
@article{arxiv.2506.11805,
title = {Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula},
author = {Li-Juan Cheng and Rui-Yu Yang},
journal= {arXiv preprint arXiv:2506.11805},
year = {2025}
}
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