English

Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups

Analysis of PDEs 2022-06-30 v2

Abstract

We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with H\"{o}lder continuous coefficients. The kernels appearing in the integrals are supported on the level and superlevel sets of the fundamental solution relevant 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 perimeters on stratified Lie groups.

Keywords

Cite

@article{arxiv.2204.11541,
  title  = {Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups},
  author = {Diego Pallara and Sergio Polidoro},
  journal= {arXiv preprint arXiv:2204.11541},
  year   = {2022}
}

Comments

19 pages

R2 v1 2026-06-24T10:57:34.772Z