Homogenization of Nonlinear Degenerate Non-monotone Elliptic Operators in Domains Perforated with Tiny Holes |
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Authors: | Jean Louis Woukeng |
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Institution: | 1.Department of Mathematics and Computer Science,University of Dschang,Dschang,Cameroon |
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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 Ω
ε
in ℝ
N
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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Keywords: | |
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