manuscripta mathematica

, Volume 112, Issue 4, pp 473–487 | Cite as

Regularity of generalized sphere valued p-harmonic maps with small mean oscillations

  • Paweł StrzeleckiEmail author


We prove (see Theorem 1.3 below) that a generalized harmonic map into a round sphere, i.e. a map uW 1,1 loc (Ω,𝕊 n−1 ) which solves the system \({{ {{{{\rm{ div}}}}}(u^i\nabla u^j - u^j\nabla u^i) =0,{{\quad}}\!i,j=1,\ldots,n, }}\) is smooth as soon as |∇u|∈L q for any q>1, and the norm of u in BMO is sufficiently small. Here, Ω⊂ℝ m is open, and m,n are arbitrary. This extends various earlier results of Almeida [1], Ge [15], and R. Moser [38]. A version of this result for generalized p-harmonic maps into spheres is also proved. The proofs rely on the duality of Hardy space and BMO combined with L p stability of the Hodge decomposition and reverse Hölder inequalities.


Early Result Hardy Space Round Sphere Hodge Decomposition Generalize Sphere 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Institute of MathematicsWarsaw UniversityWarszawaPoland

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