MEAN VALUE FORMULAS FOR CLASSICAL SOLUTIONS TO SOME DEGENERATE ELLIPTIC EQUATIONS IN CARNOT GROUPS

We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with Holder continuous coefficients. The kernels appearing in the integrals are supported on the level and superlevel sets of the fundamental solution relative the adjoint differential operator. We then extend the aforementioned formulas to some subelliptic operators on Carnot groups. In this case we rely on the theory of finite perimeter sets on stratified Lie groups.

Automated summary

This paper proves surface and volume mean value formulas for classical solutions to uniformly elliptic equations with Holder continuous coefficients. It extends the formulas to subelliptic operators on Carnot groups, relying on the theory of finite perimeter sets on stratified Lie groups.