Mean value formulas for classical solutions to uniformly parabolic equations in divergence form

Emanuele Malagoli, Diego Pallara, Sergio Polidoro

Published 2021-09-02Version 1

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in divergence form. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C^1-boundary, the other stated for sets with finite perimeter.