γ-Convergence of integral functionals and the variational dirichlet problem in variable domains

By using special local characteristics of domains Ω _s ⊂Ω,s=12,..., we establish necessary and sufficient conditions for the γ-convergence of sequences of integral functionalsI _λs :W ^k,m (Ω _s )→ℝ, λ⊂Ω to interal functionals defined on W ^k,m (Ω). Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1236–1254, September, 1996.