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The periodic unfolding method for perforated domains and Neumann sieve models

Abstract : The periodic unfolding method, introduced in [D. Cioranescu, A. Damlamian, G. Griso, Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99-1041, was developed to study the limit behavior of periodic problems depending on a small parameter E. The same philosophy applies to a range of periodic problems with small parameters and with a specific period (as well as to almost any combinations thereof). One example is the so-called Neumann sieve. In this work, we present these extensions and show how they apply to known results and allow for generalizations (some in dimension N >= 3 only). The case of the Neumann sieve is treated in details. This approach is significantly simpler than the original ones, both in spirit and in practice. (c) 2007 Elsevier Masson SAS. All rights reserved.
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D. Cioranescu, Alain Damlamian, G. Griso, D. Onofrei. The periodic unfolding method for perforated domains and Neumann sieve models. Journal de Mathématiques Pures et Appliquées, Elsevier, 2008, 89 (3), pp.248--277. ⟨10.1016/j.matpur.2007.12.008⟩. ⟨hal-00693074⟩

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