An Epsilon-regularity result for Generalized Harmonic Maps into Spheres
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For m, n ≥ 2 and 1 < p < 2, we prove that a map u ∈ W1,ploc (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 . The proof is based on an inverse Hölder inequality technique.
CitationMoser, R. (2003). An epsilon-regularity result for generalized harmonic maps into spheres. Electronic Journal of Differential Equations, 2003(01), pp. 1-7.
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