Rigorous derivation of nonlinear plate theory and geometric rigidity

We show that nonlinear plate theory arises as a P-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps v : (0, 1)(3) --> R-3. We show that the L-2 distance of delv from a single rotation is bounded by a multiple of the L-2 distance from the set SO(3) of all rotations. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.