Reinforcement of a Muticonnected Domain by a Thin Layer of Oscillating Thickness

This work considers a reinforcement of a multiconnected domain representing the cross section of a cylindrical bar. Dirichlet boundary condition is imposed on its outer boundary and integral condition on its inner boundary. We assume that the reinforcement is periodic and has small thickness which is of the same order as the period. We describe the limiting behaviour of the reinforced structure as the period goes to zero.linear elliptic problem.