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arXiv · 1210.7340

On Lp Estimates in Homogenization of Elliptic Equations of Maxwell's Type

Zhongwei Shen·Liang Song
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Abstract

For a family of second-order elliptic systems of Maxwell's type with rapidly oscillating periodic coefficients in a $C^{1, α}$ domain $Ω$, we establish uniform estimates of solutions $u_\varep$ and $\nabla \times u_\varep$ in $L^p(Ω)$ for $1<p\le \infty$. The proof relies on the uniform $W^{1,p}$ and Lipschitz estimates for solutions of scalar elliptic equations with periodic coefficients.

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Zhongwei Shen, Liang Song. 2012-10-27. On Lp Estimates in Homogenization of Elliptic Equations of Maxwell's Type. https://arxiv.org/abs/1210.7340

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