Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 01, pp. 1-7.
Title: An $\epsilon$-regularity result for generalized
harmonic maps into spheres
Author: Roger Moser (MPI for Math. in the Sciences, Leipzig, Germany)
Abstract:
For $m,n \ge 2$ and $1 < p < 2$, we prove that a map
$u \in
W_\mathrm{loc}^{1,p}(\Omega,\mathbb{S}^{n - 1})$
from an open domain $\Omega \subset \mathbb{R}^m$
into the unit $(n - 1)$-sphere, which solves
a generalized version of the harmonic map equation,
is smooth, provided that $2 - p$ and
$[u]_{\mathrm{BMO}(\Omega)}$ are both sufficiently
small.
This extends a result of Almeida [1].
The proof is based
on an inverse Holder inequality technique.
Submitted December 13, 2002. Published January 2, 2003.
Math Subject Classifications: 58E20.
Key Words: Generalized harmonic maps; regularity.