F. Ferrari - E. M. Merlino
Lipschitz regularity for almost minimizers of a one-phase $p$-Bernoulli-type functional in Carnot Groups of step two
Published Paper
Inserted: 19 oct 2026
Last Updated: 19 oct 2026
Journal: Advances in Calculus of Variations
Volume: 19
Number: 4
Pages: 511-554
Year: 2026
Doi: https://doi.org/10.1515/acv-2025-0024
Abstract:
In this paper, in a Carnot group $\mathbb{G}$ of step $2$ and homogeneous dimension $Q$, we prove that almost minimizers of the (horizontal) one-phase $p$-Bernoulli-type functional
\[J_p(u,Ω):=\int_Ω\Big(
\nabla_{\mathbb{G}}u(x)
^p+χ_{\{u>0\}}(x)\Big)\,dx\] whenever $p>p^\#:=\frac{2Q}{Q+2}$, are locally Lipschitz continuous with respect Carnot-Carathéodory distance on $\mathbb{G}$.