Duality and compactness results in high-contrast homogenization of incompressible two-dimensional elasticity problems
David Manceau · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2009
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 $L^2_\mathrm{loc}$ for a sequence of two-dimensional vector-valued functions in $H^1_0$ which are only bounded in L2.