On Entire Solutions of the System Laplacian of u - grad W(u)=0, u from Rn to Rn

We establish existence for potentials with a finite number of global minima and symmetric under a finite reflection group, plus other conditions. We also make some basic observations that do not require any symmetry: A Sress Tensor T that allows the system to be written as DivT=0, a weak monotonocity formula, and a Liouville type Theorem.