Reference : Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and h...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds
Chen, Qin-Qian [Zhejiang University of Technology > Department of Applied Mathematics]
Cheng, Li-Juan [Hangzhou Normal University > School of Mathematics]
Thalmaier, Anton mailto [University of Luxembourg > Department of Mathematics]
In press
Stochastic Partial Differential Equations: Analysis and Computations
29 pp
[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.
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