随机系数抛物型方程的点态双尺度展开
Pointwise two-scale expansion for parabolic equations with random coefficients
摘要：
研究了随机系数线性抛物型方程均匀化中的一阶修正。在尺寸$3$和更高的系数有一个有限的依赖范围内，我们证明了一个逐点版本的两个规模的扩展。对于散度型的椭圆型方程，也得到了类似的展开式。这个结果是令人惊讶的，因为如果没有对系数定律的进一步对称性假设，它就不会是真的。
英文摘要：
We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of the two-scale expansion. A similar expansion is derived for elliptic equations in divergence form. The result is surprising, since it was not expected to be true without further symmetry assumptions on the law of the coefficients.
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