A counterexample to the monotone increasing behavior of an Alt-Caffarelli-Friedman formula in the Heisenberg group

Abstract

In this paper we provide a counterexample about the existence of an increasing monotonicity behavior of a function introduced in \cite{FeFo}, companion of the celebrated Alt-Caffarelli-Friedman monotonicity formula, in the noncommutative framework.

References in corpus (1)

• Some remarks about the existence of an Alt-Caffarelli-Friedman monotonicity formula in the Heisenberg group

Cited by in corpus (1)

• Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications