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

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

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 smo...

Full description

Bibliographic Details
Main Author: Junichi Aramaki
Format: Article
Language:English
Published: Texas State University 2014-01-01
Series:Electronic Journal of Differential Equations
Subjects:
Harmonic maps
minimizing harmonic maps
weak Harnack inequality
Online Access:http://ejde.math.txstate.edu/Volumes/2014/34/abstr.html
Description
Summary: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".
ISSN:1072-6691

Similar Items