G-convergence of cyclically monotone operators

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 a_h of maximal monotone operators of this type, the convergence of the sequence of the solutions u_h to the equations −div(a_h(x,Du_h))=f_h implies the convergence of the corresponding momenta a_h(x,Du_h) in spite of the fact that the functions a_h are nonlinear. The equivalence between the Γ-convergence of certain integral functionals and the G-convergence of the corresponding sub differentials is also established.