Periodic homogenization for inner boundary conditions with equi-valued surfaces: the unfolding approach

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 — dimensional rod with a multiply-connected cross section as well as for the general electroconductivity 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

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