Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications
Analysis of PDEs
2023-10-23 v1
Abstract
In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we show that our argument holds in the general framework of Carnot groups.
Keywords
Cite
@article{arxiv.2310.13264,
title = {Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications},
author = {Fausto Ferrari and Nicolò Forcillo},
journal= {arXiv preprint arXiv:2310.13264},
year = {2023}
}