G-convergence of cyclically monotone operators

Article type: Research Article

Authors: Defranceschi, Anneliese

Affiliations: International School for Advanced Studies, Strada Costiera 11, 34014 Trieste, Italy

Abstract: The paper deals with equations of the form −div(a(x,Du))=f, where a(x,ξ) is cyclically monotone. The main result is that, given a sequence ah of maximal monotone operators of this type, the convergence of the sequence of the solutions uh to the equations −div(ah(x,Duh))=fh implies the convergence of the corresponding momenta ah(x,Duh) in spite of the fact that the functions ah are nonlinear. The equivalence between the Γ-convergence of certain integral functionals and the G-convergence of the corresponding sub differentials is also established.

DOI: 10.3233/ASY-1989-2103

Journal: Asymptotic Analysis, vol. 2, no. 1, pp. 21-37, 1989