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

Multiple Integrals under Di erential Constraints: Two-Scale Convergence and Homogenization

Two-scale techniques are developed for sequences of maps {uk} ⊂ L(Ω; R ) satisfying a linear di erential constraint Auk = 0. These, together with Γconvergence arguments and using the unfolding operator, provide a homogenization result for energies of the type

Homogenization and Two - Scale Convergence *

Following an idea of G. Nguetseng, the author defines a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector-type theorem (i.e., which permits, in some cases, replacing a sequence by its "two-scale" limit, up to a st...

Two-Scale Convergence and Homogenization of Periodic Structures

Homogenization of Integral Energies under Periodically Oscillating Differential Constraints

A homogenization result for a family of integral energies uε 7→ ˆ Ω f(uε(x)) dx, ε → 0, is presented, where the fields uε are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity with variable coefficients and on twoscale convergence techniques.

Periodic Homogenization of Integral Energies under Space-dependent Differential Constraints

A homogenization result for a family of oscillating integral energies uε 7→ ˆ Ω f(x, x ε , uε(x)) dx, ε → 0 is presented, where the fields uε are subjected to first order linear differential constraints depending on the space variable x. The work is based on the theory of A -quasiconvexity with variable coefficients and on two-scale convergence techniques, and generalizes the previously obtaine...