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Networks and Heterogeneous Media

2008, Volume 3, Issue 3: 509-522. doi: 10.3934/nhm.2008.3.509
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Duality results in the homogenization of two-dimensional high-contrast conductivities

  • 1.
    Centre de Mathématiques INSA de Rennes & IRMAR, 20 ave. des Buttes de Coësmes, 35043 Rennes Cedex
  • 2.
    I.R.M.A.R., Université de Rennes 2, Rennes Cedex
  • Received: 01 January 2008

  • Primary: 35J25, 35B27; Secondary: 35B25.

  • The paper deals with some extensions of the Keller-Dykhneduality relations arising in the classical homogenization of two-dimensional uniformly bounded conductivities, to the case of high-contrast conductivities. Only assuming a L1-bound on the conductivity we prove that the conductivity and its dual converge respectively, in a suitable sense, to the homogenized conductivity and its dual. In the periodic case a similar duality result is obtained under a less restrictive assumption.

    Citation: Marc Briane, David Manceau. Duality results in the homogenization of two-dimensional high-contrast conductivities[J]. Networks and Heterogeneous Media, 2008, 3(3): 509-522. doi: 10.3934/nhm.2008.3.509

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  • The paper deals with some extensions of the Keller-Dykhneduality relations arising in the classical homogenization of two-dimensional uniformly bounded conductivities, to the case of high-contrast conductivities. Only assuming a L1-bound on the conductivity we prove that the conductivity and its dual converge respectively, in a suitable sense, to the homogenized conductivity and its dual. In the periodic case a similar duality result is obtained under a less restrictive assumption.


  • This article has been cited by:

    1. Mohamed Camar-Eddine, Laurent Pater, Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures, 2013, 8, 1556-181X, 913, 10.3934/nhm.2013.8.913
    2. 2009, 978-1-4398-0175-8, 289, 10.1201/9781439801765-b
    3. Marc Briane, Laurent Pater, Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three, 2012, 393, 0022247X, 563, 10.1016/j.jmaa.2011.12.059
    4. Liya Gaynutdinova, Martin Ladecký, Ivana Pultarová, Jan Zeman, Guaranteed lower bounds to effective stiffness, 2023, 23, 1617-7061, 10.1002/pamm.202300098
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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