Prépublication du DMI numéro 02-01 (18/02/2002)

Stability of Slopes and Subdifferentials
GEOFFROY, Michel - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97157 cedex
LASSONDE, Marc - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97157 cedex

We show that the slope introduced by DeGiorgi-Marino-Tosques in 1980 is stable (in a sense to be precised) with respect to the variational convergence introduced by the authors in 2000. Applications to the stability of subdifferentials are derived, including a further characterization of slice-convergence of convex functions in terms of set convergence of enlargements of their subdifferentials.