The nonlinear membrane model: Variational derivation under the constraint "det$\nabla u\ne 0$"

Abstract

Acerbi, Buttazzo and Percivale gave a variational definition of the nonlinear string energy under the constraint "det$\nabla u>0$" (see [1]). In the same spirit, we obtain the nonlinear membrane energy under the simpler constraint "det$\nabla u\ne 0$".

16 pages, submitted to Journal de Mathematiques pures et appliquees on 8 October, 2004