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

Abstract

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).