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

Ruiqi Jiang

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arXiv · 1301.1014

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

Ruiqi Jiang

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Abstract

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.

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BibTeX RIS

Ruiqi Jiang. 2013-01-06. Harmonic Maps with Potential from $\mathbb{R}^2$ into $S^2$. https://arxiv.org/abs/1301.1014

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