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G-convergence of cyclically monotone operators. (English) Zbl 0681.47023
Author’s summary: The paper deals with equations of the form \[ - div(a(x,Du))=f, \] where a(x,\(\xi)\) 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 \(\Gamma\)-convergence of certain integral functions and the G- convergence of the corresponding subdifferentials is also established.
Reviewer: J.Appell

47H05 Monotone operators and generalizations
47F05 General theory of partial differential operators
35A35 Theoretical approximation in context of PDEs