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

In: Partial Differential Equations: Theory, Control and Approximation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Doina Cioranescu & Alain Damlamian & Tatsien Li, 2014. "Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces: The Unfolding Approach," Springer Books, in: Philippe G. Ciarlet & Tatsien Li & Yvon Maday (ed.), Partial Differential Equations: Theory, Control and Approximation, edition 127, pages 183-209, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-41401-5_7
    DOI: 10.1007/978-3-642-41401-5_7
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