New counterexamples to the cell formula in nonconvex homogenization

Marco Barchiesi (1) , Antoine Gloria (2, 3)

1 CMU - Carnegie Mellon University [Pittsburgh]
2 ULB - Département de Mathématique [Bruxelles]
3 SIMPAF - SImulations and Modeling for PArticles and Fluids

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.

Mots clés: homogenization; quasiconvexity; cell problem

Domaines: Equations aux dérivées partielles [math.AP]; Bibliothèque électronique [cs.DL]

Marco Barchiesi, Antoine Gloria. New counterexamples to the cell formula in nonconvex homogenization. Archive for Rational Mechanics and Analysis, 2010, 195, pp.991-1204. ⟨10.1007/s00205-009-0226-9⟩. ⟨hal-00767100⟩