  A periodic connection is constructed for a double well potential defined in
the plane. This solution violates Modica's estimate as well as the
corresponding Liouville Theorem for general phase transition potentials.
Gradient estimates are also established for several kinds of elliptic systems.
They allow us to prove in some particular cases the Liouville Theorem. Finally,
we give an alternative form of the stress-energy tensor for solutions defined
in planar domains. As an application, we deduce a (strong) monotonicity
formula.
