Abstract
In this article we extend the ideas presented in Onofrei and Vernescu [Asymptotic Anal. 54 (2007), pp. 103–123] and introduce suitable second-order boundary layer correctors, to study the H
1-norm error estimate for the classical problem of homogenization, i.e.
Previous second-order boundary layer results assume either smooth enough coefficients (which is equivalent to assuming smooth enough correctors χ
j
, χ
ij
∈
W
1,∞), or smooth homogenized solution
u
0, to obtain an estimate of order
. For this we use some ideas related to the periodic unfolding method proposed by Cioranescu et al. [
C. R. Acad. Sci. Paris, Ser. I 335 (2002), pp. 99–104]. We prove that in two dimensions, for non-smooth coefficients and general data, one obtains an estimate of order
. In three dimensions the same estimate is obtained assuming χ
j
, χ
ij
∈
W
1,p
, with
p > 3.
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