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