In this paper we give a general proof of Mean Value formulas for solutions to second order linear PDEs, only based on the local properties of their fundamental solution Gamma. Our proof requires a kind of pointwise vanishing integral condition for the intrinsic gradient of Gamma. 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.
Cupini, G., Lanconelli, E. (2021). On Mean Value formulas for solutions to second order linear PDEs. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 22(2), 777-809 [10.2422/2036-2145.201904_014].
On Mean Value formulas for solutions to second order linear PDEs
Cupini, G;Lanconelli, E
2021
Abstract
In this paper we give a general proof of Mean Value formulas for solutions to second order linear PDEs, only based on the local properties of their fundamental solution Gamma. Our proof requires a kind of pointwise vanishing integral condition for the intrinsic gradient of Gamma. 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.| File | Dimensione | Formato | |
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