椭圆偏微分方程均质化中平均格林函数的正则性
On regularity of averaged Green's functions in homogenization of elliptic PDE
浏览论文内容
中文总结 AI 辅助
本文利用Bourgain的洞见，在更一般情形下证明了随机系数椭圆偏微分方程均质化中平均格林函数的二阶导数估计。
中文摘要 AI 辅助
本文关注于在$d$维整数格$\mathbb{Z}^d$上具有随机系数的均匀椭圆散度形式偏微分方程的平均格林函数的估计。先前已证明，在大尺度下，平均格林函数被均质化格林函数逐点良好逼近。相应的结果也适用于平均格林函数的（分数阶）导数，直至但不包括二阶导数。当椭圆方程生成正半群时（如对角情形），二阶导数结果已建立。此处，利用Bourgain的洞见，更一般地证明了二阶导数结果。
英文摘要
This paper is concerned with establishing estimates on averaged Green's functions for a uniformly elliptic divergence form partial difference equation with random coefficients on the $d$ dimensional integer lattice $\mathbb{Z}^d$. It has previously been shown that the averaged Green's function is point-wise well approximated by the homogenized Green's function at large length scales. Corresponding results also hold for (fractional) derivatives of the averaged Green's function up to but not including the second derivative. Second derivative results have been established when the elliptic equation generates a positive semi-group, as in the diagonal case. Here the second derivative result is shown more generally by using an insight of Bourgain.
发表机构
- University of Michigan（密歇根大学）
- University of Michigan-Dearborn（密歇根大学迪尔伯恩分校）
机构由 AI 辅助整理，请以论文原文为准。
