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

  title={Homogenization for Non-self-adjoint Periodic Elliptic Operators on an Infinite Cylinder},
  author={Nikita N. Senik},
  journal={SIAM J. Math. Anal.},
  • N. N. Senik
  • Published 20 August 2015
  • Mathematics, Computer Science
  • SIAM J. Math. Anal.
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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