Uniform Estimates in Homogenization: Compactness Methods and Applications

Prange, Christophe

Journées équations aux dérivées partielles (2014), article no. 7, 25 p.

The purpose of this note is to explain how to use compactness to get uniform estimates in the homogenization of elliptic systems with or without oscillating boundary. Along with new results in this direction, we highlight some important applications to pointwise estimates of Green and Poisson kernels, to the homogenization of boundary layer systems and to the boundary control of composite materials.

Mots clés : Homogenization, compactness methods, boundary layers, potential theory, Green kernel, Poisson kernel, control of distributed systems

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