Homogenization of Elliptic Systems with Neumann Boundary Conditions

Details Homogenization of Elliptic Systems with Neumann Boundary Conditions Homogenization of Elliptic Systems with Neumann Boundary Conditions

2010-10-29

arxiv.org/abs/1010.6114v1

Mathematics

Analysis of PDEs

39 pages

Scientific paper

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.

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