Subdifferentiation of integral functionals

Emmanuel Giner (1) , Jean-Paul Penot (2)

1 UT3 - Université Toulouse III - Paul Sabatier
2 LJLL - Laboratoire Jacques-Louis Lions

We examine how the subdi¤erentials of nonconvex integral functionals can be deduced from the subdi¤erentials of the corresponding integrand or at least be estimated with the help of them. In fact, assuming some regularity properties of the integrands, we obtain exact expressions for the subdi¤erentials of the integral functionals. We draw some consequences in terms of duality for such integral functionals, extending in this way the early work of R.T. Rockafellar to the nonconvex case.

Mots clés: integral functional; integrand; Legendre function; regularity; subdi¤erential Mathematics Subject Classi…cation 28C99; 49J52; 58Cxx; 46G05

Domaines: Mathématiques [math]

Emmanuel Giner, Jean-Paul Penot. Subdifferentiation of integral functionals. 2017. ⟨hal-01450022⟩