Homogenization of the Poisson equation in a thick periodic junction (Q1969392)

Summary: A convergence theorem and asymptotic estimates as \(\varepsilon\to 0\) are proved for a solution to a mixed boundary value problem for the Poisson equation in a junction \(\Omega_\varepsilon\) of a domain \(\Omega_0\) and a large number \(N^2\) of \(\varepsilon\)-periodically situated thin cylinders with thickness of order \(\varepsilon=O ({1\over N})\). For this junction, we construct an extension operator and study its properties.