Concentration and homogenization in composites with total flux interface conditions

The model analyzed in this paper describes a composite made by a hosting medium containing a periodic array of inclusions, of size $\eps$, coated by a thin layer of a different material with thickness of the order $\eps\eta$. The thin layer presents an inner interface with imperfect contact conditions of non-local type. We deal with the concentration of the coating layer and with the homogenization, via the periodic unfolding method, of the resulting model. The construction of the homogenized matrix and of the limit source term deserves a deep investigation, despite the fact that the limit problem looks like a standard Dirichlet problem for an elliptic equation.