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Homogenization of elliptic systems with periodic coefficients: operator error estimates in $L_2(\mathbb {R}^d)$ with corrector taken into account
A matrix elliptic selfadjoint second order differential operator (DO) ${\mathcal B}_{\varepsilon }$ with rapidly oscillating coefficients is considered in $L_2(\mathbb {R}^d;\mathbb {C}^n)$. The principal part $b(\mathbf {D})^* g(\varepsilon ^{-1}\mathbf {x})b(\mathbf {D})$ of this operator is given in a factorized form, where $g$ is a periodic, bounded, and positive definite matrix-valued …