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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.

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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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