In this article, we prove the continuity of the horizontal gradient near a C1,Dini non-characteristic portion of the boundary for solutions to $\Gamma ^{0,{\rm Dini}}$ perturbations of horizontal Laplaceans as in (1.1) below, where the scalar term is in scaling critical Lorentz space L(Q, 1) with Q being the homogeneous dimension of the group. This result can be thought of both as a sharpening of the $\Gamma ^{1,\alpha }$ boundary regularity result in [4] as well as a subelliptic analogue of the main result in [1] restricted to linear equations.

中文翻译：

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卡诺群边界处的边界梯度估计

在本文中，我们证明了水平梯度在 a 附近的连续性C1、迪尼解决方案的边界的非特征部分$\伽玛 ^{0,{\rm 迪尼}}$水平拉普拉斯算子的扰动，如下面的（1.1），其中标量项在缩放临界洛伦兹空间大号(问, 1) 与问是组的同质维度。这个结果可以被认为是$\伽玛 ^{1,\alpha }$[4] 中的边界规则性结果以及 [1] 中主要结果的亚椭圆类似物仅限于线性方程。