Locally minimising solutions of − Δu = u(1 − |u|2) in R2
Étienne Sandier · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1998
We prove that locally minimising solutions of − Δu = u(1 − |u|2) in R2, i.e. solutions that minimise the action in any bounded domain of R2, are such that ∫R2(1 − |u|2)2(x) dx < + ∞. We prove a similar property for locally minimising solutions in a half-plane.