1301.1014 (Ruiqi Jiang)

Harmonic Maps with Potential from $\mathbb{R}^2$ into $S^2$    [PDF]

Ruiqi Jiang

We study the existence problem of harmonic maps with potential from $\mathbb{R}^2$ into $S^2$. For a specific class of potential functions on $S^2$, we give the sufficient and necessary conditions for the existence of equivariant solutions of this problem. As an application, we generalize and improve the results on the Landau-Lifshitz equation from $\mathbb{R}^2$ into $S^2$ in \cite{G_S} due to Gustafson and Shatah.

View original: http://arxiv.org/abs/1301.1014