On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures

Davide Barilari (1) , Yacine Chitour (2) , Frédéric Jean (3) , Dario Prandi (4, 2) , Mario Sigalotti (5, 6)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 L2S - Laboratoire des signaux et systèmes
3 OC - Optimisation et commande
4 CNRS - Centre National de la Recherche Scientifique
5 CaGE - Control And GEometry
6 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

We prove the C^1 regularity for a class of abnormal length-minimizers in rank 2 sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank 2 sub-Riemannian structures of step up to 4 are of class C^1

Domaines: Optimisation et contrôle [math.OC]; Géométrie différentielle [math.DG]

Davide Barilari, Yacine Chitour, Frédéric Jean, Dario Prandi, Mario Sigalotti. On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures. Journal de Mathématiques Pures et Appliquées, 2020, 133, pp.118-138. ⟨10.1016/j.matpur.2019.04.008⟩. ⟨hal-01757343v2⟩