We shall consider harmonic maps from -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
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