Calculus of Variations and Geometric Measure Theory
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M. Barchiesi - A. Gloria

New counterexamples to the cell formula in nonconvex homogenization

created by barchiesi on 29 Aug 2008
modified on 12 Jan 2012

[BibTeX]

Published Paper

Inserted: 29 aug 2008
Last Updated: 12 jan 2012

Journal: Arch. Ration. Mech. Anal.
Volume: 195
Pages: 991-1024
Year: 2010

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.

Keywords: Homogenization, quasiconvexity, cell formula


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