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Using a physically motivated stress energy tensor, we prove weak and strongmonotonicity formulas for solutions to the semilinear elliptic system $\Deltau=\nabla W(u)$ with $W$ nonnegative. In particular, we extend a recent twodimensional result to all dimensions.

A new monotonicity formula for solutions to the elliptic system $\Delta u=\nabla W(u) $