A nonlinear variational Neumann's type problem

Abstract

In this work I consider a nonlinear Neumann's problem involving a maximal monotone operator. The existence of a H2-solution was proved in ([4]). Here I prove a weak existence theorem, the uniqueness of a weak continuous solution, the continuous dependence on the data and I state a priori estimate. At the end by applying the finite element method, I obtain approximate solutions, by means of a perturbed variational problem and an estimate of the discretization error. An algorithm is explained.