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Article Dans Une Revue Proceedings of the Royal Society of Edinburgh: Section A, Mathematics Année : 2009

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

David Manceau

Résumé

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 $L^1$ but not in $L^\infty$. A compactness result is obtained for Hooke's laws which are uniformly bounded from above and such that their inverses are bounded in $L^1$ but not in $L^\infty$, with a refinement in the periodic case. Moreover, we establish a compactness result in $L^2_\mathrm{loc}$ for a sequence of two-dimensional vector-valued functions in $H^1_0$ which are only bounded in $L^2$.

Dates et versions

hal-00747926 , version 1 (02-11-2012)

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Citer

David Manceau. Duality and compactness results in high-contrast homogenization of incompressible two-dimensional elasticity problems. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2009, 139 (5), pp.997-1015. ⟨10.1017/S0308210508000863⟩. ⟨hal-00747926⟩
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