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

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.