English

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

Analysis of PDEs 2010-10-29 v2

Abstract

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.

Cite

@article{arxiv.0909.4392,
  title  = {Some basic facts on the system \Delta u - W_u (u) = 0},
  author = {Nicholas D. Alikakos},
  journal= {arXiv preprint arXiv:0909.4392},
  year   = {2010}
}

Comments

10 pages; minor revision

R2 v1 2026-06-21T13:49:55.511Z