The limit behavior of a family of variational multiscale problems

Abstract

AbstractΓ-convergence techniques combined with techniques of 2-scale convergence are used to give a characterization of the behavior as ε goes to zero of a family of integral functionals defined onZ Ω

Multiple integrals under differential constraints: two-scale convergence and homogenization

“…We remark that the result obtained in this paper now extends that in [4] Berlyand, Cioranescu and Golovaty [5], Babadjian and Baía [3], and the references therein.…”

“…In this context, using this together with Γ-limit techniques, Baia and Fonseca in [4] obtained the integral representation for the limit energy of a family of functionals…”

A note on concentrations for integral two-scale problems

“…Using standard gamma convergence results on homogenization (see Theorem 1.1 in Baía and Fonseca [5]) and since by (7) …”

Multiscale homogenization of monotone operators

“…We refer to [10] for reiterated homogenization of degenerate nonlinear elliptic equations. For more general information on reiterated homogenization and its application, we refer to the survey article [25] (see also [3], [4], [5], [15] and [29] regarding some recent developments in this theory).…”