  Let \Omega and \tilde{\Omega} be uniformly convex domains in \mathbb{R}^n
with smooth boundary. We show that there exists a diffeomorphism f: \Omega \to
\tilde{\Omega} such that the graph \Sigma = \{(x,f(x)): x \in \Omega\} is a
minimal Lagrangian submanifold of \mathbb{R}^n \times \mathbb{R}^n.
