# Homogenization for Non-self-adjoint Periodic Elliptic Operators on an Infinite Cylinder

@article{Senik2017HomogenizationFN, title={Homogenization for Non-self-adjoint Periodic Elliptic Operators on an Infinite Cylinder}, author={Nikita N. Senik}, journal={SIAM J. Math. Anal.}, year={2017}, volume={49}, pages={874-898} }

We consider the problem of homogenization for non-self-adjoint second-order elliptic differential operators~$\mathcal{A}^{\varepsilon}$ of divergence form on $L_{2}(\mathbb{R}^{d_{1}}\times\mathbb{T}^{d_{2}})$, where $d_{1}$ is positive and~$d_{2}$ is non-negative. The~coefficients of the operator~$\mathcal{A}^{\varepsilon}$ are periodic in the first variable with period~$\varepsilon$ and smooth in a certain sense in the second. We show that, as $\varepsilon$ gets small, $(\mathcal{A…

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