An epsilon-regularity result for generalized harmonic maps into spheres
Roger Moser · DOAJ (DOAJ: Directory of Open Access Journals) · 2003
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.