Pointwise two-scale expansion for parabolic equations with random coefficients
Yu Gu, Jean-Christophe Mourrat · arXiv (Cornell University) · 2014
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.