Shell theories arising as low energy ��-limit of 3d nonlinear elasticity

We discuss the limiting behavior (using the notion of ��-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like h^4 (where h is the thickness of a shell), we derive a limiting theory which is a generalization of the von K��rm��n theory for plates.
36 pages, 1 figure