New Counterexamples to the Cell Formula in Nonconvex Homogenization

Marco Barchiesi
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213
marcob@andrew.cmu.edu



Antoine Gloria
IAM
Universität Bonn
Wegelerstr. 10
53115 Bonn, Germany

ABSTRACT: In this article we show that for the homogenization of multiple integrals, the quasiconvexification of the cell formula is different from the asymptotic formula in general. To this aim, we construct three examples in three different settings: the homogenization of a discrete model, the homogenization of a composite material and the homogenization of a homogeneous material on a perforated domain.

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