Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899402 | Journal of Mathematical Analysis and Applications | 2018 | 11 Pages |
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 Îu. An extension to differential forms is also given. Our approach is probabilistic and could easily be adapted to other settings.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Li-Juan Cheng, Anton Thalmaier, James Thompson,