A new monotonicity formula for solutions to the elliptic system $\Delta   u=\nabla W(u) $
  Using a physically motivated stress energy tensor, we prove weak and strong monotonicity formulas for solutions to the semilinear elliptic system $\Delta u=\nabla W(u)$ with $W$ nonnegative. In particular, we extend a recent two dimensional result to all dimensions. 
Christos Sourdis
math.AP