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.
Sweeping processes and rate independence / Recupero, Vincenzo. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - STAMPA. - 23:3(2016), pp. 921-946.