Geodesic
An $\varepsilon$-regularity result for generalized harmonic maps into spheres
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Moser, Roger},
     title = {An $\varepsilon$-regularity result for generalized harmonic maps into spheres},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a194/}
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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/