Homogenization of the Poisson Equation in a Thick Periodic Junction

Abstract

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.