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Mathematics Colloquium: Homogenization and field concentrations in heterogeneous media
4:10 p.m. TODD 125
Abstract: A multi-scale characterization of the field concentrations inside composite and polycrystalline media is developed. The talk focuses on gradient fields associated with solutions of second order elliptic PDE with measurable coefficients. A rigorous mathematical theory for assessing the Lp integrability of gradient fields inside microstructured media is developed. The results are described in terms of the pth order moments of the solution of two-scale corrector problems. Examples are provided that illustrate the theory and its application.