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

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

2011-03-29

arxiv.org/abs/1103.5721v1

Mathematics

Analysis of PDEs

Scientific paper

Let $\mathcal{L}_\epsilon$ 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)) -\deltaare sharp for $n=2$ or 3.

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