  We present a sufficient condition under which a weak solution of the
Euler-Lagrange equations in nonlinear elasticity is already a global minimizer
of the corresponding elastic energy functional. This criterion is applicable to
energies $W(F)=\widehat{W}(F^TF)=\widehat{W}(C)$ which are convex with respect
to the right Cauchy-Green tensor $C=F^TF$, where $F$ denotes the gradient of
deformation. Examples of such energies exhibiting a blow up for $\det F\to0$
are given.
