Quantitative C¹-estimates by Bismut formulae

2017/07/22 by Lijuan Cheng, Cheng, Li-Juan, Anton Thalmaier +3 · 1 citation
Mathematics · #58J05 #58J65 #60J60 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1707.07121

openalex publication_date 2017/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a C² function u and an elliptic operator L, we prove a quantitative estimate for the derivative du in terms of local bounds on u and Lu. An integral version of this estimate is then used to derive a condition for the zero-mean value property of Δu. An extension to differential forms is also given. Our approach is probabilistic and could easily be adapted to other settings.

Cited by

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

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