Duality results in the homogenization of two-dimensional high-contrast conductivities
Marc Briane - Centre de Mathématiques INSA de Rennes & IRMAR, 20 ave. des Buttes de Coësmes, 35043 Rennes Cedex, France (email)
Abstract: 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: Homogenization, duality in two-dimensional media, high and
low conductivities, periodic microstructures
Received: January 2008; Published: June 2008.
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