Electron. J. Diff. Equ., Vol. 2014 (2014), No. 34, pp. 1-7.

Another proof of the regularity of harmonic maps from a Riemannian manifold to the unit sphere

Junichi Aramaki

We shall consider harmonic maps from $n$-dimensional compact connected Riemannian manifold with boundary to the unit sphere under the Dirichlet boundary condition. We claim that if the Dirichlet data is smooth and so-called "small", all minimizers of the energy functional are also smooth and "small".

Submitted September 16, 2013. Published January 27, 2014.
Math Subject Classifications: 58E20, 53C43, 58E30.
Key Words: Harmonic maps; minimizing harmonic maps; weak Harnack inequality.

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Junichi Aramaki
Division of Science, Faculty of Science and Engineering
Tokyo Denki University,
Hatoyama-machi, Saitama 350-0394, Japan
email: aramaki@mail.dendai.ac.jp

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