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# Zeitschrift für Analysis und ihre Anwendungen

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**Volume 18, Issue 4, 1999, pp. 953–975**

**DOI: 10.4171/ZAA/923**

Published online: 1999-12-31

Homogenization of the Poisson Equation in a Thick Periodic Junction

T.A. Mel'nyk^{[1]}(1) Kyiv University, Ukraine

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.

*Keywords: *Homogenization, asymptotic estimates, extension operators

Mel'nyk T.A.: Homogenization of the Poisson Equation in a Thick Periodic Junction. *Z. Anal. Anwend.* 18 (1999), 953-975. doi: 10.4171/ZAA/923