Multiple integrals under differential constraints: two-scale convergence and homogenization
Irene Fonseca, Stefan Kroemer · Indiana University Mathematics Journal · 2010
Two-scale techniques are developed for sequences of maps {uk} ⊂ Lp (Ω; RM) satisfying a linear differential constraint Auk = 0. These, together with Γ-convergence arguments and using the unfolding operator, provide a homogenization result for energies of the type Fε(u): = f ( x, x ε, u(x)) dx with u ∈ L p (Ω; R M), Au = 0, Ω that generalizes current results in the case where A = curl.