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Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot Groups of step two
Published 6 Nov 2023 in math.AP | (2311.02975v2)
Abstract: We prove that nonnegative almost minimizers of the horizontal Bernoulli-type functional $$ J(u,\Omega):=\int_{\Omega}\Big(|\nabla_{\mathbb{G}} u(x)|2+\chi_{{u>0}}(x)\Big)\,dx$$ are Lipschitz continuous in the intrinsic sense.
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