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Journal of Convex Analysis 23 (2016), No. 3, 921--946
Copyright Heldermann Verlag 2016

Sweeping Processes and Rate Independence

Vincenzo Recupero
Dip. di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

We introduce a new reparametrization technique for convex-valued functions of bounded variation. By means of this technique we are able to reduce discontinuous BV sweeping processes to the Lipschitz continuous case by using only tools from measure theory. In particular, from the regular case we deduce existence, continuous dependence, and convergence of the catching-up algorithm.

Keywords: Sweeping processes, differential inclusions, convex sets, Hausdorff distance, rate independence, functions of bounded variation.

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

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