# Homogenization of the Poisson Equation in a Thick Periodic Junction

### T.A. Mel'nyk

Kyiv University, Ukraine

## 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.

## Cite this article

T.A. Mel'nyk, Homogenization of the Poisson Equation in a Thick Periodic Junction. Z. Anal. Anwend. 18 (1999), no. 4, pp. 953–975

DOI 10.4171/ZAA/923