Quantitative C1-estimates by Bismut formulae

Abstract
For a

C

² function

u

and an elliptic operator

L

, we prove a quantitative estimate for the derivative

du

in terms of local bounds on

u

and

L

. 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.

The paper is available here:

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