Cheng, Li Juan[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Thalmaier, Anton[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Thompson, James[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

2017

Math arXiv

10

No

[en] 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.