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

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

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