Inserted: 9 jun 2019
Last Updated: 15 jun 2019
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.