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Homogenization of random elliptic systems with an application to Maxwell's equations

G. Barbatis

Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, Athens 15784, Greece

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I. G. Stratis

Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, Athens 15784, Greece

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, and

A. N. Yannacopoulos

Department of Statistics, Athens University of Economics and Business, 76, Patission Str., Athens 10434, Greece

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https://doi.org/10.1142/S0218202515500359Cited by:3 (Source: Crossref)

Abstract

We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homogenization by Blanc, Le Bris and Lions. An application of the abstract result is given for Maxwell's equations in random dissipative bianisotropic media.

Dedicated to Professor Christodoulos Athanasiadis on the occasion of his retirement.

Keywords:

AMSC: 35B27, 35J47, 35R60, 60H25, 60H30, 78A48, 78M40

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