Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions

The energy functional of linear elasticity is obtained as Gamma-limit of suitable rescalings of the energies of finite elasticity. The quadratic control from below of the energy density W(\nabla v) for large values of the deformation gradient \nabla v is replaced here by the weaker condition $W(\na v)\geq|\na v|^p$, for some $p>1$. Energies of this type are commonly used in the study of a large class of compressible rubber-like materials.