  We study compressible and incompressible nonlinear elasticity variational
problems in a general context. Our main result gives a sufficient condition for
an equilibrium to be a global energy minimizer, in terms of convexity
properties of the pressure in the deformed configuration. We also provide a
convex relaxation of the problem together with its dual formulation, based on
measure-valued mappings, which coincides with the original problem under our
condition.
