Duality results in the homogenization of two-dimensional high-contrast conductivities

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September 2008, 3(3): 509-522. doi: 10.3934/nhm.2008.3.509

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, France

Received January 2008 Published June 2008

Abstract
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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 $L^1$-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.

Keywords: high and low conductivities, Homogenization, duality in two-dimensional media, periodic microstructures.

Mathematics Subject Classification: Primary: 35J25, 35B27; Secondary: 35B2.

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

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