G-convergence of monotone operators

  • Valeria Chiado’ Piat

    SISSA, Strada Costiera 11, 34014 Trieste, Italy
  • Gianni Dal Maso

    SISSA, Strada Costiera 11, 34014 Trieste, Italy
  • Anneliese Defranceschi

    SISSA, Strada Costiera 11, 34014 Trieste, Italy

Abstract

A general notion of G-convergence for sequences of maximal monotone operators of the form is introduced in terms of the asymptotic behavior, as h → + ∞, of the solutions uh to the equations 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.

Résumé

On présente une notion générale de G-convergence pour des opérateurs maximaux monotones sous forme divergence. On démontre le caractère local de la G-convergence et de la G-compacité pour certaines classes d’opérateurs de ce type.

Cite this article

Valeria Chiado’ Piat, Gianni Dal Maso, Anneliese Defranceschi, G-convergence of monotone operators. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 3, pp. 123–160

DOI 10.1016/S0294-1449(16)30298-0