On properties of subdifferential mappings in Fréchet spaces

Abstract

We present conditions under which the subdifferential of a proper convex lower-semicontinuous functional in a Frechet space is a bounded upper-semicontinuous mapping. The theorem on the boundedness of a subdifferential is also new for Banach spaces. We prove a generalized Weierstrass theorem in Frechet spaces and study a variational inequality with a set-valued mapping.