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Homogenization of Elliptic Systems with Neumann Boundary Conditions (1010.6114v1)
Published 29 Oct 2010 in math.AP
Abstract: The main purpose of this work is to study uniform regularity estimates for a family of elliptic operators ${\mathcal{L}_\varepsilon, \varepsilon>0}$, arising in the theory of homogenization, with rapidly oscillating periodic coefficients. We establish sharp $W{1,p}$ estimates, Lipschitz estimates, and nontangential maximal function estimates, which are uniform in the parameter $\varepsilon$, on solutions with Neumann boundary conditions in $C{1,\alpha}$ domains.