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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

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