  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.

Analysis of PDEs