We prove the following. If f is a harmonic quasiconformal mapping between the unit ball in \(\mathbb {R}^{n}\) and a spatial domain with C^1,α boundary, then f is Lipschitz continuous in B. This generalizes some known results for n = 2 and improves some others in higher dimensional case.

中文翻译：

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单位球与具有C 1，α边界的空间域之间的拟共形调和映射

我们证明以下内容。如果f是\（\ mathbb {R} ^ {n} \）中的单位球与具有C ^1，α边界的空间域之间的调和拟偶形映射，则f是B中的Lipschitz连续。这归纳了n = 2的一些已知结果，并在高维情况下改进了其他一些结果。