3D-2D analysis of a thin film with periodic microstructure

J.-F. Babadjian L.P.M.T.M. Université Paris Nord 93430, Villetaneuse, France

and

M. Baía Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213

Abstract. The purpose of this article is to study the behavior of a heterogeneous thin film whose microstructure oscillates on a scale that is comparable to that of the thickness of the domain. The argument is based on a 3D-2D dimensional reduction through a Γ-convergence analysis, techniques of two-scale convergence and a decoupling procedure between the oscillating variable and the in-plane variable.