Abstract
In [Anza Hafsa, O., Mandallena, J.-P., The nonlinear membrane energy: variational derivation under the constraint $\det \nabla u \neq 0$, J. Math. Pures Appl. 86 (2006) 100-115] we gave a variational definition of the nonlinear membrane energy under the constraint $\det \nabla u \neq 0$. In this paper we obtain the nonlinear membrane energy under the more realistic constraint $\det \nabla u > 0$.