On Fitzpatrick’s theory and stability of flows

Abstract

The initial-value problem associated to a maximal monotone operator may be formulated as a minimization principle, on the basis of a theory that was pioneered by Brezis, Ekeland,Nayroles and Fitzpatrick. This note defines the notions of structural compactness and structural stability, and reviews results concerning the stability of maximal monotone flows under perturbations not only of data but also of the operator. This rests upon De Giorgi’ theory of $\Gamma$-convergence, and on the use of an exotic nonlinear topology of weak type.