Bubbling location for -harmonic maps and inhomogeneous Landau–Lifshitz equations
Salah Najib
ICTP, Trieste, ItalyPigong Han
Chinese Academy of Sciences, Beijing, China
![Bubbling location for $F$-harmonic maps and inhomogeneous Landau–Lifshitz equations cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-cmh.png&w=3840&q=90)
Abstract
Let be a positive smooth function on a closed Riemann surface . The -energy of a map from to a Riemannian manifold is defined as
In this paper, we will study the blow-up properties of Palais–Smale sequences for . We will show that, if a Palais–Smale sequence is not compact, then it must blow up at some critical points of . As a consequence, if an inhomogeneous Landau–Lifshitz system, i.e. a solution of
blows up at time , then the blow-up points must be the critical points of .
Cite this article
Salah Najib, Pigong Han, Bubbling location for -harmonic maps and inhomogeneous Landau–Lifshitz equations. Comment. Math. Helv. 81 (2006), no. 2, pp. 433–448
DOI 10.4171/CMH/57