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Homogenization of Nonlinear Degenerate Non-monotone Elliptic Operators in Domains Perforated with Tiny Holes

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Abstract

The paper deals with the homogenization problem beyond the periodic setting, for a degenerated nonlinear non-monotone elliptic type operator on a perforated domain Ωε in ℝN with isolated holes. While the space variable in the coefficients a 0 and a is scaled with size ε (ε>0 a small parameter), the system of holes is scaled with ε 2 size, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The homogenization problem is formulated in terms of the general, so-called deterministic homogenization theory combining real homogenization algebras with the Σ-convergence method. We present a new approach based on the Besicovitch type spaces to solve deterministic homogenization problems, and we obtain a very general abstract homogenization results. We then illustrate this abstract setting by providing some concrete applications of these results to, e.g., the periodic homogenization, the almost periodic homogenization, and others.

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  1. Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Jean Louis Woukeng

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  1. Jean Louis Woukeng
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Woukeng, J.L. Homogenization of Nonlinear Degenerate Non-monotone Elliptic Operators in Domains Perforated with Tiny Holes. Acta Appl Math 112, 35–68 (2010). https://doi.org/10.1007/s10440-009-9552-z

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  • DOI: https://doi.org/10.1007/s10440-009-9552-z

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