G-convergence of monotone operators

A general notion of G-convergence for sequences of maximal monotone operators of the form [Figure presented] is introduced in terms of the asymptotic behavior, as h → + ∞ of the solutions uh to the equations [Figure presented] and of their momenta ah(x, Duh). The main results of the paper are the local character of the G-convergence and the G-compactness of some classes of nonlinear monotone operators. © 2016 L'Association Publications de l'Institut Henri Poincaré