A general sufficient condition for avoiding infimum-gaps when the domain of an optimal control problem is densely embedded in a larger family of processes is here presented. This condition generalizes some recently estalished cryteria for convex or impulsive embedding, and is based on "abundantness" a dynamics-related notion of density introduced by J. Warga.
We will present results on the minimal time function where the velocity sets are locally the same.
joint work with Carlo Mariconda
We consider the classical problem of the Calculus of Variations, and we formulate of a new Weierstrass-type condition for local minimizers of the reference problem. It allows to derive important properties for a broad class of problems involving a nonautonomous, possibly extended-valued, Lagrangian. A first consequence is the validity of a Du Bois-Reymond type necessary condition, expressed in terms of convex subgradients. If the Lagrangian satisfies an additional growth condition (weaker than coercivity), this Weierstrass-type condition yields the Lipschitz regularity of the minimizers.