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arXiv · 2311.02975

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

Fausto Ferrari·Nicoló Forcillo·Enzo Maria Merlino
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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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Fausto Ferrari, Nicoló Forcillo, Enzo Maria Merlino. 2023-11-06. Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot Groups of step two. https://arxiv.org/abs/2311.02975

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