Approximation of resolvents in homogenization of fourth-order elliptic operators

We study the homogenization of a fourth-order divergent elliptic operator $A_\varepsilon$ with rapidly oscillating $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. The homogenized operator $A_0$ is of the same type and has constant coefficients. We apply Zhikov's shift method to obtain an estimate in the $(L^2\to L^2)$-operator norm of order $\varepsilon^2$ for the difference of the resolvents $(A_\varepsilon+1)^{-1}$ and $(A_0+1)^{-1}$.
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