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, \\ u=0, cases where is an open bounded subset of RN (N 2) with Lipschitz boundary, m>0, and f belongs to the Lorentz space L^N, (). 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.