Semiconcavity results for optimal control problems admitting no singular minimizing controls
Snakes and articulated arms in an Hilbert space
The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.
Strutture subriemanniane in alcuni problemi di Analisi
Vengono presentati alcuni problemi, idee e tecniche sorte nell'ambito della teoria delle equazioni alle derivate parziali del secondo ordine, con forma caratteristica semidefinita positiva e con soggiacenti strutture sub-riemanniane. Se ne traccia lo sviluppo a partire dalla classica teoria delle funzioni armoniche e caloriche, attraverso la teoria del potenziale negli spazi armonici astratti e la teoria della regolarità locale delle soluzioni.
Subriemannian geodesics of Carnot groups of step 3
In Carnot groups of step ≤ 3, all subriemannian geodesics are proved to be normal. The proof is based on a reduction argument and the Goh condition for minimality of singular curves. The Goh condition is deduced from a reformulation and a calculus of the end-point mapping which boils down to the graded structures of Carnot groups.
Sub-riemannian metrics : minimality of abnormal geodesics versus subanalyticity
Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlinéaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating...