Maëlle Labeille

Imagine a ball bouncing on the ground. If you slow down time, the mecanics of the bounce are well-known: the ball is represented as an elastic solid, it slightly flattens on impact with the floor, then recovers its shape and bounces on the opposite direction. But what if you don't slow down time? At impact, the ball's velocity instantly goes from downward to upward. At impact, the force and acceleration are instantaneous, with infinite value: it is a Dirac measure. Within this context, I will present the space of functions whose derivatives are measures, called functions of bounded variations.