Geodesic
Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev class $H^1(\mathbb R^d)$
Algebra i analiz, Tome 18 (2006) no. 6, pp. 1-130 
M. Sh. Birman; T. A. Suslina. Homogenization with corrector for periodic differential operators. Approximation of solutions in the Sobolev class $H^1(\mathbb R^d)$. Algebra i analiz, Tome 18 (2006) no. 6, pp. 1-130. http://geodesic.mathdoc.fr/item/AA_2006_18_6_a0/
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     title = {Homogenization with corrector for periodic differential operators. {Approximation} of solutions in the {Sobolev} class~$H^1(\mathbb R^d)$},
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     url = {http://geodesic.mathdoc.fr/item/AA_2006_18_6_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Investigation of a class of matrix periodic elliptic second-order differential operators $\mathcal A_\varepsilon$ in $\mathbb R^d$ with rapidly oscillating coefficients (depending on $\mathbf x/\varepsilon$) is continued. The homogenization problem in the small period limit is studied. Approximation for the resolvent $(\mathcal A_\varepsilon+I)^{-1}$ in the operator norm from $L_2(\mathbb R^d)$ to $H^1(\mathbb R^d)$ is obtained with an error of order $\varepsilon$. In this approximation, a corrector is taken into account. Moreover, the ($L_2\to L_2$)-approximations of the so-called fluxes are obtained.

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