Published Paper

Inserted: 17 jan 2024
Last Updated: 29 jul 2024

Journal: Annali di Matematica Pura ed Applicata (1923 -)
Year: 2024
Doi: https://doi.org/10.1007/s10231-024-01490-8

Abstract:

In this paper we continue the analysis of an Alt-Caffarelli-Friedman (ACF) monotonicity formula in Carnot groups of step $s >1$ confirming the existence of counterexamples to the monotone increasing behavior. In particular, we provide a sufficient condition that implies the existence of some counterexamples to the monotone increasing behavior of the ACF formula in Carnot groups. The main tool is based on the lack of orthogonality of harmonic polynomials in Carnot groups. This paper generalizes the results proved in \cite{ferrari2023counterexample}.