Existence of sweeping process in Banach spaces under directional   prox-regularity
  This paper is devoted to weaken "classical" assumptions and give new arguments to prove existence of sweeping process (associated to the proximal normal cone of sets). Mainly we define the concept of a "directional prox-regularity" and give assumptions about a Banach space to insure the existence of such sweeping process (which permit to generalize the existing results requiring a Hilbertian structure). 
Frederic Bernicot (LM-Orsay), Juliette Venel (LM-Orsay)