Quantitative C1-estimates by Bismut formulae
by Li-Juan Cheng, Anton Thalmaier and James Thompson

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 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:

Li-Juan Cheng
Anton Thalmaier
James Thompson

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