Journal of Convex Analysis 17 (2010), No. 2, 451--484
Copyright Heldermann Verlag 2010
Differential Inclusions with Proximal Normal Cones in Banach Spaces
Frédéric Bernicot
Dép. de Mathématiques, Université de Paris-Sud, 91405 Orsay, France
frederic.bernicot@math.u-psud.fr
Juliette Venel
Dép. de Mathématiques, Université de Paris-Sud, 91405 Orsay, France
juliette.venel@math.u-psud.fr
This paper is devoted to weaken "classical" assumptions and to give new arguments to prove existence of solutions of differential inclusions with proximal normal cones in Banach spaces. Mainly we define the concept of "directional prox-regularity" and give assumptions on a Banach space to ensure the existence of such differential inclusions (which permits to generalize existing results requiring a Hilbertian structure).
Keywords: Differential inclusion, sweeping process, prox-regularity, proximal normal cone.
MSC: 34A60, 49J52, 58C20
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