# American Institute of Mathematical Sciences

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

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.
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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