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Séminaire du LJLL : P. Cannarsa
20 février 2015 — 14h00
Piermarco Cannarsa (Université de Rome 2 Tor Vergata)
Dynamique singulière pour les équations d’Hamilton-Jacobi
Abstract
In dynamic programming, the set of points at which the value function of an optimal control problem fails to be differentiable is usually regarded as a region to keep away from. Indeed, the uniqueness of optimal trajectories is generally lost on such a set and numerical schemes become less reliable. Such a viewpoint, however, could be partly reversed thinking of the huge quantity of data that can be compressed at a singular point. This talk will be focussed on singularities of solutions to Hamilton-Jacobi equations, in connection with optimal control problems, and the dynamics that describes their propagation. We will be particularly interested in the study of the invariance of the singular set under such dynamics for two examples of solutions to eikonal-type equations: the euclidean (and riemannian) distance function from the boundary of a bounded domain and the solution of a Cauchy problem given by the Hopf-Lax formula.