On the $Γ$-Convergence of integral functionals defined on sobolev weakly connected spaces

Abstract

We introduce and study the concept of Γ-convergence of functionateI _s :W ^k,m (Ω)→ℝ,s=1,2,..., to a functional defined on (W ^k,m (Ω))² and describe the relationship between this type of convergence and the convergence of solutions of Neumann variational problems. For a sequence of integral functionateI _s :W ^k,m (Ω)→ℝ, we prove a theorem on the selection of a subsequence Γ-convergent to an integral functional defined on (W ^k,m (Ω))²