G-convergence of monotone operators. (English) Zbl 0731.35033

Summary: A general notion of G-convergence for sequences of maximal monotone operators of the form \({\mathcal A}_ hu=-div(a_ h(x,Du))\) is introduced in terms of the asymptotic behavior, as \(h\to +\infty\), of the solutions \(u_ h\) to the equations \({\mathcal A}_ hu_ h=f_ h\) and of their momenta \(a_ h(x,Du_ h)\). 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.


35J60 Nonlinear elliptic equations
47H05 Monotone operators and generalizations
35G30 Boundary value problems for nonlinear higher-order PDEs
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