Abstract
For a bounded domain Ω ⊂ R n endowed with L ∞-metric g, and a C 5-Riemannian manifold (N, h) ⊂ R k without boundary, let u ∈ W 1,2(Ω, N) be a weakly harmonic map, we prove that (1) u ∈ C α (Ω, N) for n = 2, and (2) for n ≥ 3, if, in additions, g ∈ VMO(Ω) and u satisfies the quasi-monotonicity inequality (1.5), then there exists a closed set Σ ⊂ Ω, with H n-2(Σ) = 0, such that \({u \in C^\alpha(\Omega{\setminus}\Sigma, N)}\) for some α ∈ (0, 1).
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C. Y. Wang Partially supported by NSF.
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Ishizuka, W., Wang, C.Y. Harmonic maps from manifolds of L ∞-Riemannian metrics. Calc. Var. 32, 387–405 (2008). https://doi.org/10.1007/s00526-007-0149-y
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DOI: https://doi.org/10.1007/s00526-007-0149-y