Well Posed Variational Problems and Friedrichs Extensions

In this paper the concept of well posed variational problem is studied for the pair (P, F_f where P is a multivoque operator from B(P) c X into 2 X and 3,. is a convex functiont, Convenient hypotheses show that if the variational problem for the pair (P, 3 p) is well will then P can be extended up to a maximal monotone and surjective operator. Several applitint A (“temperature control” included) are also considered.