论文标题
非线性均匀椭圆方程的随机均质化中高阶线性化的校正估计值
Corrector estimates for higher-order linearizations in stochastic homogenization of nonlinear uniformly elliptic equations
论文作者
论文摘要
校正器估计构成了通过均匀椭圆方程的均匀化理论中的两尺度扩展技术推导最佳收敛速率的关键要素。根据校正估计，本工作在Fischer和Neukamm（Arxiv：1908.02273）的最新工作中进行了跟进，该工作提供了在光谱隙假设下的非线性椭圆形方程的定量随机均质化理论。我们为高阶线性化校正器建立了最佳级估计（相对于显微镜和宏观尺度之间的比例缩放）。校正器估计值的一个相当简单的结果是相关均质单调操作员的高阶规则性。
Corrector estimates constitute a key ingredient in the derivation of optimal convergence rates via two-scale expansion techniques in homogenization theory of random uniformly elliptic equations. The present work follows up - in terms of corrector estimates - on the recent work of Fischer and Neukamm (arXiv:1908.02273) which provides a quantitative stochastic homogenization theory of nonlinear uniformly elliptic equations under a spectral gap assumption. We establish optimal-order estimates (with respect to the scaling in the ratio between the microscopic and the macroscopic scale) for higher-order linearized correctors. A rather straightforward consequence of the corrector estimates is the higher-order regularity of the associated homogenized monotone operator.
