Calculus of Variations and Geometric Measure Theory
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G. Cupini - E. Lanconelli

On Mean Value formulas for solutions to linear second order PDEs

created by cupini on 09 Jun 2019
modified on 15 Jun 2019

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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.


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