Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 34, pp. 1-7.

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

Author: Junichi Aramaki (Tokyo Denki Univ., Saitama, Japan)

Abstract:
 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.