论文标题
$ \ varepsilon $ scale平面域中的椭圆系统的规律性理论
Regularity theory of elliptic systems in $\varepsilon$-scale flat domains
论文作者
论文摘要
我们以定期振荡系数的差异形式考虑线性椭圆系统或方程。我们证明了满足所谓的$ \ varepsilon $ scale平面度的域中弱解决方案的大规模边界Lipschitz估算值，该条件可以任意低于$ \ varepsilon $ -Scale。这特别概括了Kenig和Prange在[32]和[33]中的工作，并通过定量方法进行了概括。
We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called $\varepsilon$-scale flatness condition, which could be arbitrarily rough below $\varepsilon$-scale. This particularly generalizes Kenig and Prange's work in [32] and [33] by a quantitative approach.
