An Epsilon-regularity result for Generalized Harmonic Maps into Spheres

Abstract

For m, n ≥ 2 and 1 < p < 2, we prove that a map u ∈ W1,p loc (Ω, Sn-1) from an open domain Ω ⊂ ℝm into the unit (n - 1)-sphere, which solves a generalized version of the harmonic map equation, is smooth, provided that 2 - p and [u] BMO(Ω) are both sufficiently small. This extends a result of Almeida [1]. The proof is based on an inverse Hölder inequality technique.