Existence of sweeping process in Banach spaces under directional prox-regularity

Frédéric Bernicot (1) , Juliette Venel (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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).

Mots clés: Sweeping process; prox-regularity; proximal normal cone

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]

Frédéric Bernicot, Juliette Venel. Existence of sweeping process in Banach spaces under directional prox-regularity. Journal of Convex Analysis, 2010, 17 (2), pp.451-484. ⟨hal-00349506⟩