Homogenization of the Poisson Equation in a Thick Periodic Junction

Abstract

A convergence theorem and asymptotic estimates as $ϵ\to 0$ are proved for a solution to a mixed boundary-value problem for the Poisson equation in a junction ${\Omega }_{ϵ}$, of a domain ${\Omega }_0$ and a large number $N^2$ of $ϵ$-periodically situated thin cylinders with thickness of order $ϵ=O(\frac{1}{N})$. For this junction, we construct an extension operator and study its properties.