The periodic unfolding method for a class of imperfect transmission problems

Abstract

The periodic unfolding method was introduced by D. Cioranescu, A. Damlamian and G. Griso for studying the classical periodic homogenization in fixed domains and more recently extended to periodically perforated domains by D. Cioranescu, A. Damlamian, P. Donato, G. Griso, and R. Zaki. Here, the method is adapted to two-component domains which are separated by a periodic interface. The unfolding method is then applied to an elliptic problem with a jump of the solution on the interface, which is proportional to the flux and depends on a real parameter. We prove some homogenization and corrector results, which recover and complete those previously obtained by the first author and S. Monsurrò. Bibliography: 32 titles. Illustrations: 2 figures. © 2011 Springer Science+Business Media, Inc.