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.
Supported by the National Natural Science Foundation of China (No. 11121101) and the National Basic Research Program of China (No. 2013CB834100).
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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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Cioranescu, D., Damlamian, A., Li, T. (2014). Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces: The Unfolding Approach. In: Ciarlet, P., Li, T., Maday, Y. (eds) Partial Differential Equations: Theory, Control and Approximation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41401-5_7
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