F. Ferrari - N. Forcillo - E. M. Merlino
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot Groups of step two
Published Paper
Inserted: 19 oct 2026
Last Updated: 19 oct 2026
Journal: Calculus of Variations and Partial Differential Equations
Volume: 64
Number: 107
Year: 2025
Doi: https://doi.org/10.1007/s00526-025-02959-x
Abstract:
We prove that nonnegative almost minimizers of the horizontal Bernoulli-type functional
\[J(u,Ω):=\int_Ω\Big(
\nabla_{\mathbb{G}} u(x)
^2+χ_{\{u>0\}}(x)\Big)\,dx\] are Lipschitz continuous in the intrinsic sense.