论文标题
$ \ MATHSCR {C}^1 $平滑Jordan域之间的谐波准表面映射
Harmonic quasiconformal mappings between $\mathscr{C}^1$ smooth Jordan domains
论文作者
论文摘要
我们证明了以下结果。如果$ f $是两个Jordan域$ d $和$ω$之间具有$ \ mathscr {c}^1 $边界的谐音准图形映射，那么函数$ f $在全球范围内连续$α<1 <1 $，但总体上不是Lipschitz。这扩展并改善了S. warschawski的经典定理用于保形映射。
We prove the following result. If $f$ is a harmonic quasiconformal mapping between two Jordan domains $D$ and $Ω$ having $\mathscr{C}^1$ boundaries, then the function $f$ is globally Hölder continuous for every $α<1$ but it is not Lipschitz in general. This extends and improves a classical theorem of S. Warschawski for conformal mappings.
