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Journal of Convex Analysis 27 (2020), No. 2, 535--556
Copyright Heldermann Verlag 2020

Convex Valued Geodesics and Applications to Sweeping Processes with Bounded Retraction

Vincenzo Recupero
Dip. di Scienze Matematiche, Politecnico di Torino, 10129 Torino, Italy

We provide a formulation for sweeping processes with arbitrary locally bounded retraction, not necessarily left or right continuous. Moreover we provide a proof of the existence and uniqueness of solutions for this formulation which relies on the reduction to the 1-Lipschitz continuous case by using a suitable family of geodesics for the asymmetric Hausdorff-like distance called excess.

Keywords: Evolution variational inequalities, functions of bounded variation, sweeping processes, convex sets, retraction, geodesics with respect to the excess.

MSC: 34G25, 34A60, 47J20, 74C05.

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