Geodesic
An \(\varepsilon\)-regularity result for generalized harmonic maps into spheres
Electronic journal of differential equations, Tome 2003 (2003)
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.
Classification : 58E20
Keywords: generalized harmonic maps, regularity 
@article{EJDE_2003__2003__a194,
     author = {Moser,  Roger},
     title = {An \(\varepsilon\)-regularity result for generalized harmonic maps into spheres},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1018.58007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a194/}
}
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%J Electronic journal of differential equations
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Moser,  Roger. An \(\varepsilon\)-regularity result for generalized harmonic maps into spheres. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a194/