Uniqueness for elliptic problems with locally Lipschitz continuous dependence on the solution

We consider a class of elliptic equations of the type−div(a(x,u,∇u))=f−divg with Dirichlet boundary conditions and with f belonging to L1(Ω). Using the framework of renormalized solutions we prove the uniqueness of a solution when the usual Lipschitz condition on the function a is relaxed.