Uniform W^{1,p} Estimates for Systems of Linear Elasticity in a Periodic Medium

Let $\mathcal{L}_ε$ be a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients. We obtain the uniform $W^{1,p}$ estimate in a Lipschitz domain for solutions to the Dirichlet problem, where $(2n/(n+1)) -δ<p<(2n/(n-1))+δ$. The ranges of $p$'s are sharp for $n=2$ or 3.

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