Homogenization of materials with defects

We present some recent mathematical contributions related to homogenization problems. The difficulty stems from the fact that the medium is not assumed periodic, but has a structure with a set of embedded defects, localized or not, or more generally a structure that, although not periodic, enjoys nice geometrical features. The purpose is then to construct a theoretical setting providing an efficient and accurate approximation of the multiscale solution. The questions raised range from the theory of PDEs (elliptic or not, linear or not) and homogenization theory to harmonic analysis and singular operators. Computational issues are also discussed.

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