On the homogenization of a Signorini-type problem in a domain with inclusions

In this paper we investigate the effect of a Signorini-type interface condition on the asymptotic behaviour, as ε tends to zero, of problems posed in ε-periodic domains with inclusions. The Signorini-type condition is expressed in terms of two complementary equalities involving the jump of the solution on the interface and its conormal derivative via a parameter γ. Our problem models the heat exchange in a medium hosting an ε-periodic array of thermal conductors in presence of impurities distributed on some regions of the interface. Different limit problems are obtained according to different values of γ.