Existence and regularity of solutions for the elliptic nonlinear transparent media equation

In this paper we study existence and regularity of solutions to Dirichlet problems as cases - div(|u|ᵐD u/|D u|) = f & in\;Ω,\\ u=0 & on\;∂Ω, cases where Ω is an open bounded subset of RN (N≥ 2) with Lipschitz boundary, $m>0$, and f belongs to the Lorentz space LN,∞(Ω). In particular, we explore the regularizing effect given by the degenerate coefficient |u|ᵐ in order to get non-trivial and bounded solutions with no smallness assumptions on the size of the data.