Some basic facts on the system ∆u - W_u (u) = 0
Nicholas D. Alikakos · arXiv (Cornell University) · 2009
Abstract. We rewrite the system ∆u − Wu(u) = 0, for u: R n → 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. 1.