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Journal of Function Spaces and Applications
Volume 7, Issue 2, Pages 121-152
http://dx.doi.org/10.1155/2009/102486

Reiterated homogenization of nonlinear monotone operators in a general deterministic setting

1Narvik University College, P.O. Box 385, N-8505 Narvik, Norway
2Norut Narvik, P.O. Box 250, N-8504 Narvik, Norway
3Department of Mathematics, University of Yaounde I, P.O. Box 812 Yaounde, Cameroon
4University of Yaounde I, Ecole Normale Supérieure, P.O. Box 47 Yaounde, Cameroon
5Department pf Mathematics, Luleå Technological University, S-97187 Luleå, Sweden

Received 1 January 2008

Academic Editor: Björn Birnir

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study reiterated homogenization of a nonlinear non-periodic elliptic differential operator in a general deterministic setting as opposed to the usual stochastic setting. Our approach proceeds from an appropriate notion of convergence termed reiterated Σ-convergence. A general deterministic homogenization theorem is proved and several concrete examples are studied under various structure hypotheses ranging from the classical periodicity hypothesis to more complicated, but realistic, structure hypotheses.