Asymptotic analysis of a spectral problem in a periodic thick junction of type 3:2:1

Abstract

Convergence theorems and asymptotic estimates (as #epsilon##->#0) are proved for eigenvalues and eigenfunctions of a mixed boundary-value problem for the Laplace operator 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(N"-"1). For this junction we construct the extension operator that is only asymptotically bounded in #epsilon# on the eigenfunctions in the Sobolev space H"1. (orig.)