$\Gamma$-Stability of maximal monotone processes

Abstract

The flow of noncyclic maximal monotone operators is formulated variationally as null-minimization problems, via results of Brezis, Ekeland, Nayroles and Fitzpatrick. By means of De Giorgi’s theory of $\Gamma$-convergence, the compactness and the stability of these flows are derived under nonparametric perturbations of the operator. These results are here reviewed, and are applied to quasilinear equations arising in electromagnetism.