The nonlinear membrane model: Variational derivation under the constraint "det$\nabla u\not=0$"

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101190Acerbi, 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$\nabla u\not=0$".16 pages, submitted to Journal de Mathematiques pures et appliquees on 8 October, 2004Classical Analysis and ODEs49J45; 74K15The nonlinear membrane model: Variational derivation under the constraint "det$\nabla u\not=0$"text