Integration formulas via the Legendre-Fenchel Subdifferential of nonconvex functions

Starting from explicit expressions for the subdiferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the "-subdi§erential and the Legendre-Fenchel subdiferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction of the lsc convex envelope either in terms of the "-subdi§erential of the nominal function or of the subdiferential of its weak lsc envelope.