We show that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps ν : (0, 1)3 → ℝ3. We show that the L2 distance of ∇ν from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations.
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Acknowledgements. RDJ thanks AFOSR/MURI (F49620-98-1-0433), ARO (DAAG55-98-1-0335), NSF (DMS-0074043) and ONR (N00014-99-1-0925) for supporting his work. GF and SM were partially supported by the TMR network FMRX-CT98-0229.