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{\bf The Cosserat Vector in Membrane Theory:  A variational Approach}

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Guy Bouchitt\'e\\
D\'epartement de Math\'ematiques\\
 Universit\'e du Sud-Toulon-Var BP 132\\
83957 La Garde Cedex, France\\
bouchitte@univ-tln.fr

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Irene Fonseca\\
Department of Mathematicla Sciences\\
Carnegie Mellon Unviersity\\
Pittsburgh, PA  15213\\
fonseca@andrew.cmu.edu

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M. Luisa Mascarenhas\\
Departamento de Matem\'atica da F.C.T.-U.N.L. e C.M.A-U.N.L.\\
Quinta da Torre\\
2829-516 Caparica, Portugal\\
mascar@fct.unl.pt
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\noindent {\bf Abstract}:  In a previous article (see [BFM]) the autors
studied a model of nonlinear membrane where the external surface loading
induces a density of bending moment.  Due to the special form of the applied
surface forces, the emerging Cosserat vector, resulting from the 3D-2D
dimension reduction, was restricted to a class of two dimensional functions.
In the paper the full 3D dependence of the Cosserat vector is analyzed via
$\Gamma$-convergence techniques. 

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