We prove the existence of infinitely many vector-valued Lipschitz-continuous functions u on an open set Ω satisfying suitable Dirichlet boundary conditions such that the singular values of the gradient matrix ∇u, agree a.e. on Ω with N given positive, bounded and lower semicontinuous functions.
Functions with prescribed singular values of the gradient / P., Celada; Perrotta, Stefania. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 5:(1998), pp. 383-396.