In this paper, we will investigate a multiscale homogenization theory for a second-order elliptic problem with rapidly oscillating periodic coefficients of the form . Noticing the fact that the classic homogenization theory presented by Oleinik has a high demand for the smoothness of the homogenization solution , we present a new estimate for the homogenization method under the weaker smoothness that homogenization solution satisfies than the classical homogenization theory needs.

中文翻译：

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具有快速振荡周期系数的二阶椭圆问题均匀化方法的一种新估计

在本文中，我们将研究具有以下形式的快速振荡周期系数的二阶椭圆问题的多尺度均匀化理论 . 注意到Oleinik提出的经典均质化理论对均质化解的平滑度要求较高，在均质化解满足比经典均质化理论需要的更弱的平滑度下，我们对均质化方法提出了新的估计。