Error estimate of the second-order homogenization for divergence-type nonlinear elliptic equation

Abstract

Second-order two-scale expansions, a unified proof for the regularity of the correctors based on the translation invariant and a lemma for extracting $O(\epsilon )$ from the remainder term are presented for the second order nonlinear elliptic equation with rapidly oscillating coefficients. If the data are smooth enough, the error of the zero-order (or energy) in $L^{\infty }$, first-order in the Hölder norm, (linear periodic case)second-order's(even first-order's) gradient (or flux) in the maximum norm,are locally $O(\epsilon )$. It can be used in the parabolic equation.

arXiv comment3 pages, a part of the first author's doctoral dissertation