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

Outline Abstract Keywords MSC 1. Introduction 2. Setting of the problem and main result 3. Existence and uniqueness result 4. The periodic unfolding method 5. Proof of the homogenization result Acknowledgement Appendix A Data availability References Show full outline Figures (1) Fig. 1. The two-component domain Ω and the reference cell Y. Abstract 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 domains with ε-periodically distributed inclusions. The Signorini-type condition is expressed in terms of a set of equalities and inequalities involving the jump of the solution on the interface and its conormal derivative via a parameter γ. Different limit problems are obtained according to different values of γ. More precisely, for γ<−1 we get the homogenized problem of Bensoussan-Lions-Papanicolau in a fixed domain while for −1<γ<1, we obtain the homogenized problem of Cioranescu-S.J. Paulin in the case of a perforated domain with Neumann condition on the boundary of the holes. The most interesting cases are γ=−1 and γ=1, where the limit problem is nonlinear and defined via a cell variational inequality, or it appears as an obstacle problem, respectively.