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.

中文翻译：

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关于高阶椭圆系统齐次化的算子估计

摘要

在空间\(\mathbb R^d\)中，我们考虑具有可测量\(\varepsilon\)周期系数的任意偶数阶\(2m\ge 4\)的矩阵椭圆算子\(L_\varepsilon\)，其中\(\varepsilon\)是一个小参数。我们构造该算子的求解的近似值，其算子\((L^2\to L^2) \) -范数中的误差为 \( \varepsilon^ 2\)量级。