Questions related to the homogenization of the Dirichlet problem for nondivergence elliptic equations of second order with rapidly oscillating $$\varepsilon$$ -periodic coefficients are studied. Error estimates of homogenization in the Sobolev spaces of order $$\sqrt\varepsilon$$ are obtained. Asymptotic homogenization methods are applied.

中文翻译：

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二阶非发散椭圆算子的均匀化估计

研究了与具有快速振荡 $$\varepsilon$$ - 周期系数的二阶非发散椭圆方程的 Dirichlet 问题的均质化相关的问题。获得了 $$\sqrt\varepsilon$$ 阶 Sobolev 空间中同质化的误差估计。应用渐近均质化方法。