In this paper, we study the boundary differentiability for infinity harmonic functions at some general corner points. We prove the slope estimate and provide a necessary and sufficient condition of the boundary differentiability for infinity harmonic function at less than $\pi$ corner points or greater than $\pi$ corner points (as defined in the Introduction). The boundary differentiable conclusions of the homogeneous infinity Laplace equations also apply to the inhomogeneous case.

中文翻译：

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无穷拉普拉斯方程的逐点边界可微性

在本文中，我们研究了在某些一般角点处无穷次谐波函数的边界可微性。我们证明了斜率估计，并为无限谐波函数提供了小于小于的边界微分的充要条件。 $\pi$ 拐角点或大于 $\pi$ 拐角点（在简介中定义）。齐次无穷拉普拉斯方程的边界可微结论也适用于不齐次情况。