Given a set E in R^{N * n}, set Omega subsets of R^n and a map phi:Omega -> R^N we discuss the existence of Lipschitz map u: Omega -> R^N solving

nabla(u) in E (in Omega)

u=phi (on boundary of Omega)

A specially significant case is when N=n and E=O(n) which

will lead us to immersions and origamis.

This is a joint work with P. MARCELLINI and E. PAOLINI.