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Duality and compactness results in high-contrast homogenization of incompressible two-dimensional elasticity problems

Published online by Cambridge University Press:  21 September 2009

David Manceau
Affiliation:
Laboratoire Jean Kuntzmann, Université Joseph Fourier Grenoble, BP 53, 38041 Grenoble Cedex 9, France (david.manceau@imag.fr)

Abstract

We study incompressible two-dimensional elasticity problems with high-contrast coefficients. The Keller–Dykhne duality relations are extended to the case of Hooke's laws which are equicoercive and uniformly bounded in L1 but not in L∞. A compactness result is obtained for Hooke's laws which are uniformly bounded from above and such that their inverses are bounded in L1 but not in L∞, with a refinement in the periodic case. Moreover, we establish a compactness result in for a sequence of two-dimensional vector-valued functions in which are only bounded in L2.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2009

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Duality and compactness results in high-contrast homogenization of incompressible two-dimensional elasticity problems
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