О G-сходимости нелинейных эллиптических операторов, связанных с задачей Дирихле в переменных областях

Abstract

A notion of G-convergence of operators As:Ws→W∗s to the operator A:W→W∗ is introduced and studied under certain connection conditions for the Banach spaces Ws,s=1,2,..., and the Banach space W. It has been established that the connection conditions for abstract space are satisfied by the Sobolev spaces W∘k,m(Ωs),W∘k,m(Ω) ({Ωs} is a sequence of perforated domains contained in a bounded domain Ω⊂ℝn). Hence, the results obtained for abstract operators can be applied to the operators of Dirichlet problems in the domains Ωs.