Electron. J. Diff. Eqns., Vol. 2003(2003), No. 01, pp. 1-7.

An $\epsilon$-regularity result for generalized harmonic maps into spheres

Roger Moser

Abstract:
For $m,n \ge 2$ and $1 less than p less than 2$, we prove that a map $u \in W_{\rm loc}^{1,p}(\Omega,\mathbb{S}^{n - 1})$ 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 $[u]_{{\rm BMO}(\Omega)}$ 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.

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Roger Moser
MPI for Mathematics in the Sciences
Inselstr. 22-26, D-04103 Leipzig, Germany
e-mail: moser@mis.mpg.de

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