论文标题
Calderon-Zygmund估算有限Lipschitz域上随机椭圆系统的估计
Calderon-Zygmund estimates for stochastic elliptic systems on bounded Lipschitz domains
论文作者
论文摘要
与随机同质化理论引起的具有固定的随机系数和有界相关域的固定随机系数有关，本文主要致力于研究Calderón-Zygmund估计。作为一种应用，我们分别从振荡和波动的意义上获得了均质化误差。这些结果是最佳的，达到数量$ o（\ ln（1/\ varepsilon））$，这是由校正器在尺寸二的量化二级线性和边界平滑度较低的量化的量子线引起的。在本文中，我们发现了一种新型的\ emph {minimal radius}的形式，当我们采用Gloria-Neukamm-Otto的策略最初受到NADDAF和Spencer的开创性工作的启发时，它被证明是对边界价值问题进行定量随机均质化的合适工具。
Concerned with elliptic operators with stationary random coefficients of integrable correlations and bounded Lipschitz domains, arising from stochastic homogenization theory, this paper is mainly devoted to studying Calderón-Zygmund estimates. As an application, we obtain the homogenization error in the sense of oscillation and fluctuation, respectively. These results are optimal up to a quantity $O(\ln(1/\varepsilon))$, which is caused by the quantified sublinearity of correctors in dimension two and the less smoothness of the boundary. In this paper, we find a novel form of \emph{minimal radius}, which is proved to be a suitable tool for quantitative stochastic homogenization on boundary value problems, when we adopt Gloria-Neukamm-Otto's strategy originally inspired by the pioneering work of Naddaf and Spencer.
