Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces: The Unfolding Approach
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.
KeywordsPeriodic homogenization Elastic torsion Equi-valued surfaces Resistivity well-logging Periodic unfolding method
Mathematics Subject Classification35B27 74Q05 74E30 74Q15 35J25 35Q72
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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