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Homogenization of elliptic systems with periodic coefficients: Weighted $L^p$ and $L^{\infty}$ estimates for asymptotic remainders
The difference between the fundamental matrix for a second order selfadjoint elliptic system with sufficiently smooth periodic coefficients and the fundamental matrix for the corresponding homogenized system in $\mathbb R^n$ is shown to decay as $O(1+|x|^{1-n}$) at infinity, $n\ge 2$. As a consequence, weighted $L^p$ and $L^{\infty }$ estimates are …