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

preprint2014arXivOpen access

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

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

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

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