Abstract:
In the space $\mathbb R^d$, we consider matrix elliptic operators $L_\varepsilon$ of arbitrary even order $2m\ge 4$ with measurable $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. We construct an approximation to the resolvent of this operator with an error of the order of $\varepsilon^2$ in the operator $(L^2\to L^2)$-norm.
Keywords:homogenization, approximation to the resolvent, higher-order elliptic system.
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