[en] In this article, we develop a martingale approach to localized Bismut-type Hessian formulas for heat semigroups on Riemannian manifolds. Our approach extends the Hessian formulas established by
Stroock (1996) and removes in particular the compact manifold restriction. To demonstrate the potential of these formulas, we give as application explicit quantitative local estimates for the Hessian of the heat semigroup, as well as for harmonic functions on regular domains in Riemannian manifolds.
Disciplines :
Mathématiques
Auteur, co-auteur :
Chen, Qin-Qian; Zhejiang University of Technology > Department of Applied Mathematics
Cheng, Li-Juan; Hangzhou Normal University > School of Mathematics
THALMAIER, Anton ; University of Luxembourg > Department of Mathematics
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds
Date de publication/diffusion :
juin 2023
Titre du périodique :
Stochastic Partial Differential Equations: Analysis and Computations
