论文标题
亚里曼尼亚大地测量学的衍生物是$ l_p $-Hölder连续
Derivatives of Sub-Riemannian Geodesics are $L_p$-Hölder Continuous
论文作者
论文摘要
本文致力于长期存在的关于亚及帝国大地测量学的平稳性的问题。我们证明，亚曼尼尼亚大地测量学的衍生物始终是$ l_p $-Hölder的连续。此外，该结果具有一些有趣的含义。其中包括（i）异常对照中的傅立叶系数的衰减，（ii）通过平滑功能近似它们的速率，（iii）庞加莱不平等的概括，以及（iv）将最短路径的紧凑嵌入到贝塞尔电位的空间中。
This article is devoted to the long-standing problem on the smoothness of sub-Riemannian geodesics. We prove that the derivatives of sub-Riemannian geodesics are always $L_p$-Hölder continuous. Additionally, this result has several interesting implications. These include (i) the decay of Fourier coefficients on abnormal controls, (ii) the rate at which they can be approximated by smooth functions, (iii) a generalization of the Poincaré inequality, and (iv) a compact embedding of the set of shortest paths into the space of Bessel potentials.
