Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Vincenzo Recupero

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

vincenzo.recupero@polito.it

Keywords

  • Sweeping processes
  • differential inclusions
  • convex sets
  • Hausdorff distance
  • rate independence
  • functions of bounded variation

Mathematics Subject Classification

34G25, 34A60, 47J20, 74C05

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Suggested citation

V. Recupero. “Sweeping Processes and Rate Independence.” Journal of Convex Analysis 23 (2016), No. 3, 921–946. https://doi.org/10.68381/jca23035

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