Abstract
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 Lp-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.
Funder
Ministry of Science and Higher Education of the Russian Federation
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Reference16 articles.
1. Agrachev A.A., On the equivalence of different types of local minima in sub-Riemannian problems, in Proceedings of the 37th IEEE Conference on Decision and Control.
2. Agrachev A.A., Barilari D. and Boscain U., A Comprehensive Introduction to Sub-Riemannian Geometry (2019).
3. On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures
4. Belotto da Silva A., Figalli A., Parusiński A. and Rifford L., Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3. ArXiv e-prints (2018). arXiv:1810.03347
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