For deformations that are weak limits of one-to-one maps, the neo-Hookean energy is lower semicontinuous for p between half the dimension and n-1, and minimizers exist.
Ball, Convexity conditions and existence theorems in nonlinear elasticity,Arch
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Mission $p<n-1$: Possible -- Nonlinear Elasticity Beyond Conventional Limits
For deformations that are weak limits of one-to-one maps, the neo-Hookean energy is lower semicontinuous for p between half the dimension and n-1, and minimizers exist.