Seminar on partial differential equations

Homogenization in the presence of defects

We will present some results on homogenization for linear elliptic equation. The geometry will be assumed to be either a perturbation of a periodic background, or an interface between two periodic media. In both cases, we study the homogenization problem, prove existence of a corrector, and use to build a two-scale expansion of the solution. We prove convergence estimates of this two-scale expansion.
These are a joint works with C. Le Bris (Ecole des Ponts, Paris), P.-L. Lions (Collège de France, Paris) and M. Josien (Ecole des Ponts, Paris).