微分方程齐性化理论是研究微分方程中高频率振荡的系数对解的影响，是方程研究的重要课题。由于近年来Kenig、林芳华、申仲伟等学者在非光滑区域上椭圆齐性化问题上的突破，使得这方面的研究越来越多地受到了分析学家们的重视。本项目申请者拟运用调和分析的方法和技巧来从事椭圆边值问题齐性化理论方面的研究。包括：(i)非光滑区域上 Legendre-Hadamard条件下椭圆算子的Dirichlet边值问题的齐性化理论；(ii)非光滑区域上非一致振荡系数的二阶椭圆算子的齐性化理论；（iii）Lipschitz区域上弹性系统的Neumann边值问题的齐性化理论。

Homogenization theory studies the effects of high-frequency oscillations in the coefficient upon solutions of PDE. Recently, Kenig,Lin and Shen had a big breakthrough on elliptic homogenization theory on nonsmooth domain. More and more analysts pay attention to the field. We will apply harmonic analysis methods and techniques to continue the research for elliptic homogenization problem, including (i) Homogenization problems of elliptic systems satisfying Legendre-Hadamard condition with Dirichlet boundary condtions on nonsmooth domain;(ii)Homogenization of second order elliptic operators with non-uniformly oscillating coefficients on nonsmooth domain; (iii) Homogenization of elastic systems with Neumann boundary condtions on Lipschitz domain.