Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot Groups of step two
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.
math.AP↗