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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

Marc Briane 1, and  David Manceau 2,

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.
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 and Heterogeneous Media, 2008, 3 (3) : 509-522. doi: 10.3934/nhm.2008.3.509
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