Error estimates for periodic homogenization with non-smooth coefficients

In this paper we present new results regarding the H1 0 -norm error estimate for the classical problem in homogenization using suitable boundary layer correctors. Compared with all the existing results on the subject, which assume either smooth enough coefficients or smooth data, we use the periodic unfolding method and propose a new asymptotic series to approximate the solution uε with an error estimate which holds true for nonsmooth coefficients and general data.