论文标题
加权$ l^2 $估计Lipschitz域中椭圆均匀化的估计值
Weighted $L^2$ Estimates for Elliptic Homogenization in Lipschitz Domains
论文作者
论文摘要
我们为加权$ l^p $估算开发了一种新的可实现方法。该方法适用于Lipschitz域中加权$ W^{1，2} $估计的研究，用于二阶椭圆系统的弱解，具有有限的可测量系数。它产生了必要且充分的条件，这取决于重量功能，因为加权$ w^{1,2} $估计值以给定的重量固定在固定的Lipschitz域中。使用这种条件，对于迅速振荡，周期性和VMO系数的Lipschitz结构域中的椭圆系统，我们将加权估计值的问题减少到恒定系数的情况下。
We develop a new real-variable method for weighted $L^p$ estimates. The method is applied to the study of weighted $W^{1, 2}$ estimates in Lipschitz domains for weak solutions of second-order elliptic systems in divergence form with bounded measurable coefficients. It produces a necessary and sufficient condition, which depends on the weight function, for the weighted $W^{1,2}$ estimate to hold in a fixed Lipschitz domain with a given weight. Using this condition, for elliptic systems in Lipschitz domains with rapidly oscillating, periodic and VMO coefficients, we reduce the problem of weighted estimates to the case of constant coefficients.
