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arXiv · 2206.03238

Lipschitz regularity of almost minimizers in one-phase problems driven by the $p$-Laplace operator

Serena Dipierro·Fausto Ferrari·Nicolò Forcillo·Enrico Valdinoci
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Abstract

We prove that, given~$p>\max\left\{\frac{2n}{n+2},1\right\}$, the nonnegative almost minimizers of the nonlinear free boundary functional $$ J_p(u,\Omega):=\int_{\Omega}\Big( |\nabla u(x)|^p+\chi_{\{u>0\}}(x)\Big)\,dx$$ are Lipschitz continuous.

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Serena Dipierro, Fausto Ferrari, Nicolò Forcillo, Enrico Valdinoci. 2022-06-07. Lipschitz regularity of almost minimizers in one-phase problems driven by the $p$-Laplace operator. https://arxiv.org/abs/2206.03238

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