Homogenization of Linear Elliptic Problems

Abstract

Convergence theorems are proved for solutions to linear elliptic boundary-value problems in a thick multilevel junction of type 3:2:2. In the first problem, various alternating perturbed Robin boundary conditions are considered, and alternating Neumann and Dirichlet boundary conditions on the surfaces of the thin discs from different sets in the second one. The convergence of the energy integrals for each problem is also proved (this is a very useful result that gives the possibility to directly obtain results for optimal control problems involving thick multilevel junctions).