Abstract
Let ω be a simply-connected domain in R2 and let (Eαβ) and (Fαβ) be two symmetric 2×2 matrix fields with components in L2(ω). In this Note, we identify nonlinear compatibility conditions “of Donati type” that the components Eαβ and Fαβ must satisfy in order that there exists a vector field (η1,η2,w)∈H01(ω)×H01(ω)×H02(ω) such that:12(∂αηβ+∂βηα+∂αw∂βw)=Eαβand∂αβw=Fαβin ω. The left-hand sides of these relations are the components of tensors found in the Kirchhoff–von Kármán–Love theory of nonlinearly elastic plates.
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