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Homogenization of a mixed boundary condition

We study the asymptotic behavior of the periodically mixed boundary value problem. The Dirichlet and Neumann boundary conditions are non- homogeneous and periodically mixed with small period ε. Using asymptotic analysis with respect to ε≪1, we derive an asymptotic approximation that has boundary condition of the Robin type. We justify the obtained condition by proving an appropriate error estimate.

Periodic boundary condition ; homogenization ; boundary layer ; Laplace equation ; Zaremba problem

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