On Mean Value formulas for solutions to second order linear PDEs

被引：0

作者：

Cupini, Giovanni ^{[1
]}

Lanconelli, Ermanno ^{[1
]}

机构：

[1] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy

来源：

ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE | 2021年 / 22卷 / 02期

关键词：

HARNACK INEQUALITY; VALUE PROPERTY; PRINCIPLE; EQUATIONS; KERNELS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：777 / 809

页数：33

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