Homogenization of the Poisson Equation in a Thick Periodic Junction

A convergence theorem and asymptotic estimates as $\epsilon \to 0$ are proved for a solution to a mixed boundary-value problem for the Poisson equation in a junction $\Omega_{\epsilon}$, of a domain $\Omega_0$ and a large number $N^2$ of $\epsilon$-periodically situated thin cylinders with thickness of order $\epsilon = O(\frac{1}{N})$. For this junction, we construct an extension operator and study its properties.