Submitted Paper
Inserted: 9 jun 2019
Last Updated: 15 jun 2019
Year: 2019
Abstract:
In this paper we give a general proof of Mean Value formulas for solutions to linear second order PDEs, only based on the local properties of the fundamental solution. Our proof requires a kind of pointwise vanishing integral condition for the intrinsic gradient of the fundamental solution. Combining our Mean Value formulas with a “descent method” due to Kuptsov, we obtain formulas with improved kernels. As an application, we implement our general results to heat operators on stratified Lie groups and to Kolmogorov operators.
Download: