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

Doina Cioranescu (), Alain Damlamian () and Tatsien Li ()
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Doina Cioranescu: Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions (UMR 7598 du CNRS)
Alain Damlamian: Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées, CNRS UMR 8050 Centre Multidisciplinaire de Créteil
Tatsien Li: Fudan University, Nonlinear Mathematical Modeling and Methods Laboratory, Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences

A chapter in Partial Differential Equations: Theory, Control and Approximation, 2014, pp 183-209 from Springer

Abstract: 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; 35B27; 74Q05; 74E30; 74Q15; 35J25; 35Q72 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-642-41401-5_7

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