Some basic facts on the system Δu - W_u (u) = 0

Details Some basic facts on the system Δu - W_u (u) = 0 Some basic facts on the system Δu - W_u (u) = 0

2009-09-24

arxiv.org/abs/0909.4392v2

Proc. Amer. Math. Soc. 139 (2011) 153-162

Mathematics

Analysis of PDEs

10 pages; minor revision

Scientific paper

10.1090/S0002-9939-2010-10453-7

We rewrite the system \Delta u - W_u (u) = 0, for u: R^n to R^n, in the form div T = 0, where T is an appropriate stress-energy tensor, and derive certain a priori consequences on the solutions. In particular, we point out some differences between two paradigms: the phase-transition system, with target a finite set of points, and the Ginzburg-Landau system, with target a connected manifold.

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