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MiS Preprint

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

Roger Moser


For $m,n \ge 2$ and $1 < p < 2$, we prove that a map $u \in W_{loc}^{1,p}(\Omega,S^{n - 1})$ from an open $m$-dimensional domain $\Omega$ into the unit $(n - 1)$-sphere $S^{n - 1}$, which solves a generalized version of the harmonic map equation, is smooth, provided that $2 - p$ is sufficiently small, and $u$ is small in the BMO-sense. The proof is based on an inverse Hölder inequality technique.

MSC Codes:
58E20, 35D10
generalized harmonic maps, regularity

Related publications

2003 Journal Open Access
Roger Moser

An e-regularity result for generalized harmonic maps into spheres

In: Electronic journal of differential equations, 2003 (2003), 1-7 (electronic)