Integration of Primal Lower Nice Functions in Hilbert Spaces

Abstract

In this paper, we obtain some integration results from subdifferential inclusions for primal lower nice functions by using the Moreau envelopes. A general result concerns an enlarged subdifferential inclusion. It says that, for g primal lower nice at x, the inclusion \(\partial f \subset g + \gamma \mathbb{B}\) around x entails that, for any γ′]0; γ[, f − g is γ′∈- Lipschitz continuous on an appropriate neighborhood of x.