We study homogenization of nonselfadjoint second order elliptic systems with ε-periodic rapidly oscillating coefficients as ε → 0. We obtain the L 2- and H 1-estimates for the homogenization error of order ε. The estimates admit the operator form and can be written in terms of the resolvents of the original and approximate systems in the operator norm \( {\left\Vert \cdot \right\Vert}_{L^2\to {L}^2} \) or \( {\left\Vert \cdot \right\Vert}_{L^2\to {H}^1} \). The shift method is used for obtaining such estimates.
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Translated from Problemy Matematicheskogo Analiza 89, July 2017, pp. 99-112.
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Pastukhova, S.E. Operator Estimates in Homogenization of Elliptic Systems of Equations. J Math Sci 226, 445–461 (2017). https://doi.org/10.1007/s10958-017-3543-9
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DOI: https://doi.org/10.1007/s10958-017-3543-9