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Homogenization in the Sobolev class $H^{1}(\mathbb R^{d})$ for second order periodic elliptic operators with the inclusion of first order terms
Matrix periodic elliptic second order differential operators ${\mathcal B}_{\varepsilon }$ in $\mathbb {R}^d$ with rapidly oscillating coefficients (depending on $\mathbf {x}/\varepsilon$) are studied. The principal part of the operator is given in a factorized form $b(\mathbf {D})^* g(\varepsilon ^{-1}\mathbf {x})b(\mathbf {D})$, where $g$ is a periodic, bounded and positive definite …