Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications
arXiv:2310.13264 · doi:10.1007/s40574-023-00393-5
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.