Please note the first class will be on wednesday September 10th.

The plan is to cover the following 4 parts :

1) In the first part, we will review classical results about periodic homogenization of elliptic operators. In particular we will look at : Darcy law, compensated-compactness thechniques, two scalce convergence methods, homogenization of Euler equation.

2) We will also treat few aspects of quasi-periodic, almost periodic and stochastic theories

3) Then, we will try to understand problems related to the boundary when we want to get higher order approximation. This requires a precise understanding of boundary layers

4) Finally, we will also study some rugosity problems.

Books :

1) Cioranescu, Doina; Donato, Patrizia

2) Jikov, V. V.; Kozlov, S. M.; Oleuinik, O. A.

Articles :

1) Allaire, GrĂ©goire; Amar, Micol Boundary layer tails in periodic homogenization. ESAIM Control Optim. Calc. Var. 4 (1999), 209--243

2) Moskow, Shari; Vogelius, Michael First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof. Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), no. 6, 1263--1299.

3) David G\'erard-Varet and Nader Masmoudi, Homogenization in polygonal domains (in preparation)

4) Lions, P.-L.; Masmoudi, N. Homogenization of the Euler system in a 2D porous medium. J. Math. Pures Appl. (9) 84 (2005), no. 1, 1--20.