  We consider the functional $\int_\Omega g(\nabla u+\textbf X^\ast)d\mathscr
L^{2n}$ where $g$ is convex and $\textbf X^\ast(x,y)=2(-y,x)$ and we study the
minimizers in $BV(\Omega)$ of the associated Dirichlet problem. We prove that,
under the bounded slope condition on the boundary datum, and suitable
conditions on $g$, there exists a unique minimizer which is also Lipschitz
continuous.
