P.Amster. M.Cassinelli, M.C.Mariani, D.F.Rial Existence and regularity of weak solutions to the prescribed mean curvature equation for a nonparametric surface (22K, tex) ABSTRACT. We give conditions on the boundary data and the function $h$ in order to obtain multiple solutions for the problem (1) below, using variational methods. We also study the regularity of the solutions.