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Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces: The Unfolding Approach

  • Doina Cioranescu
  • Alain Damlamian
  • Tatsien Li

Abstract

Making use of the periodic unfolding method, the authors give an elementary proof for the periodic homogenization of the elastic torsion problem of an infinite 3-dimensional rod with a multiply-connected cross section as well as for the general electro-conductivity problem in the presence of many perfect conductors (arising in resistivity well-logging). Both problems fall into the general setting of equi-valued surfaces with corresponding assigned total fluxes. The unfolding method also gives a general corrector result for these problems.

Keywords

Periodic homogenization Elastic torsion Equi-valued surfaces Resistivity well-logging Periodic unfolding method 

Mathematics Subject Classification

35B27 74Q05 74E30 74Q15 35J25 35Q72 

Notes

Acknowledgements

It was during a visit of the second author at the ISFMA that the work on this paper was started. He expresses his thanks for ISFMA’s generous support.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions (UMR 7598 du CNRS)Université Pierre et Marie CurieParisFrance
  2. 2.Laboratoire d’Analyse et de Mathématiques Appliquées, CNRS UMR 8050 Centre Multidisciplinaire de CréteilUniversité Paris-EstCréteil CedexFrance
  3. 3.Nonlinear Mathematical Modeling and Methods Laboratory, Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical SciencesFudan UniversityShanghaiChina

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