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{\bf 3D-2D analysis of a thin film with periodic microstructure}

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J.-F. Babadjian\\
L.P.M.T.M.\\
Universit\'e Paris Nord\\
93430, Villetaneuse, France\\

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and

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M. Ba\'{\i}a\\
Department of Mathematical Sciences\\
Carnegie Mellon University \\
Pittsburgh, PA  15213\\


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\noindent {\bf 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
$\Gamma$-convergence analysis, techniques of two-scale convergence and a
decoupling procedure between the oscillating variable and the in-plane
variable.

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