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

2014/02/25 by Christos Sourdis, Sourdis, Christos
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1402.6237

arxiv created 2014/02/26 · arxiv updated 2014/02/27

Abstract

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

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