On theg-convergence of nonlinear elliptic operators related to the dirichlet problem in variable domains - Kovalevskii, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
A notion of G-convergence of operators A_s : W_s → W_s^* to the operator A: W → W^* is introduced and studied under certain connection conditions for the Banach spaces W_s, 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(Ω_s),°W^k, m(Ω) ({Ω_s} is a sequence of perforated domains contained in a bounded domain Ω R^n). Hence, the results obtained for abstract operators can be applied to the operators of Dirichlet problems in the domains Ω_s.