论文标题
改进的高阶椭圆系统的均质化估计值
Improved homogenization estimates for high order elliptic systems
论文作者
论文摘要
在整个空间中，$ r^d $（$ d \ ge 2 $），我们研究了一个差异矩阵椭圆运算符的同质化$ l_ \ varepsilon $，甚至是任意订单，甚至大于2的订单，而可测量的$ \ varepsilon $ - periodic $ - periodic系数，其中$ \ varepsilon $，其中$ \ varepsilon $是一个小参数。我们强加了$ l_ \ varepsilon $的分解的近似值，其余项$ \ varepsilon^2 $在操作员$ l^2 $ -norm中。我们不超出椭圆度和系数的界限，对操作员没有规律性条件。我们使用两次秤扩展，并通过Steklov平滑规范化的校正器。
In the whole space $R^d$ ($d\ge 2$), we study homogenization of a divergence-form matrix elliptic operator $L_\varepsilon$ of an arbitrary even order larger than 2 with measurable $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. We constuct an approximation for the resolvent of $L_\varepsilon$ with the remainder term of order $\varepsilon^2$ in the operator $L^2$-norm. We impose no regularity conditions on the operator beyond ellipticity and boundedness of coefficients. We use two scale expansions with correctors regularized by the Steklov smoothing.
