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arXiv · 2506.11805

Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula

Li-Juan Cheng·Rui-Yu Yang
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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.

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Li-Juan Cheng, Rui-Yu Yang. 2025-06-13. Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula. https://arxiv.org/abs/2506.11805

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