非散度形式椭圆方程的定量随机均质化
偏微分方程分析
2019-12-10 v5 概率论
摘要
我们引入了一种研究非散度形式椭圆方程随机均质化的新方法。主要应用是一个代数误差估计，该估计断言：假设依赖范围有限，则偏离均质化极限的偏差最多与微观长度尺度的某次幂成正比。即使对于线性方程，这些结果也是新的。论证依赖于一个新的几何量，该几何量部分通过适应 Monge-Amp\`ere 方程正则性理论的要素来控制。
引用
@article{arxiv.1306.5340,
title = {Quantitative stochastic homogenization of elliptic equations in nondivergence form},
author = {Scott N. Armstrong and Charles K. Smart},
journal= {arXiv preprint arXiv:1306.5340},
year = {2019}
}
备注
40 pages. This version correctors some minor mistakes in the published version of the article, which are described in Section 1.5. Compared to v4, a typo has been fixed in (4.4) and (4.5)