Two-scale homogenization in transmission problems of elasticity with interface jumps

The elasticity problem in a periodic structure with prescribed interface jumps in displacements and tractions and oscillating Neumann condition on a part of the external boundary is considered. This work is just a generalization of inhomogeneous Dirichlet and Neumann conditions on the oscillating interface. Such interface jumps arise, e.g. in contact problems with known periodic contact interface. Two-scale approach was applied to the problem and the two-scale convergence was proven. This article also provides a detailed auxiliary analysis for Sobolev functions with interface jumps.