In this article, we want to find a map u : (Omega) over bar -> R-n solving, in Omega, the equation

u* (H) = G i.e. (Du)(t) H (u) Du = G

and coupled, on partial derivative Omega, either with the Dirichlet-Neumann problem

u = theta and Du = D theta

or the purely Dirichlet problem

where Omega subset of R-n is a bounded open set, G, H : R-n -> R-nxn and theta : (Omega) over bar -> R-n are given. We discuss the case where G and H are not necessarily symmetric or skew-symmetric, but have invertible symmetric parts. (C) 2021 Elsevier Ltd. All rights reserved.