Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 4, pp. 953975 (1999) 

Homogenization of the Poisson Equation in a Thick Periodic JunctionT. A. Mel'nykInst. Math.$\,$A Univ., PF 801140, D70511 StuttgartAbstract: A convergence theorem and asymptotic estimates as $\e \to 0$ are proved for a solution to a mixed boundaryvalue problem for the Poisson equation in a junction $\Omega_\e$ of a domain $\Omega_0$ and a large number $N^2$ of $\e$periodically situated thin cylinders with thickness of order $\e = O({1 \over N})$. For this junction, we construct an extension operator and study its properties. Keywords: homogenization, asymptotic estimates, extension operators Classification (MSC2000): 35B27, 35B40, 35B25 Full text of the article:
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