Homogenization of Quasi-Crystalline Functionals via Two-Scale-Cut-and-Project Convergence

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

Periodic homogenization for convex functionals using Mosco convergence

We study the relationship between the Mosco convergence of a sequence of convex proper lower semicontinuous functionals, defined on a reflexive Banach space, and the convergence of their subdifferentiels as maximal monotone graphs. We then apply these results together with the unfolding method (see [10]) to study the homogenization of equations of the form − div dε = f , with (∇uε(x), dε(x)) ∈ ...

Reiterated Homogenization in BV via Multiscale Convergence

Multiple-scale homogenization problems are treated in the space BV of functions of bounded variation, using the notion of multiple-scale convergence developed in [35]. In the case of one microscale Amar’s result [3] is recovered under more general conditions; for two or more microscales new results are obtained. AMS Classification Numbers (2010): 49J45, 35B27, 26A45

Two-Scale Convergence for Locally Periodic Microstructures and Homogenization of Plywood Structures

Abstract. The introduced notion of locally periodic two-scale convergence allows one to average a wider range of microstructures, compared to the periodic one. The compactness theorem for locally periodic two-scale convergence and the characterization of the limit for a sequence bounded in H1(Ω) are proven. The underlying analysis comprises the approximation of functions, with the periodicity w...