Uniqueness of a quasivariational sweeping process on functions of bounded variation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 363-394.

We prove existence and uniqueness of a quasivariational sweeping process on functions of bounded variation thereby generalizing previous results for absolutely continuous functions. It turns out that the size of the discontinuities plays a crucial role: In case they are small enough we prove existence and uniqueness. For large jumps we present a counterexample to the uniqueness of the solution. Finally we show that the condition on the jump size can be replaced by suitable conditions on the shape of the convex set.

Published online:
Classification: 49J40, 47J20, 34G25, 34C55
Roche, Thomas 1

1 Department of Mathematics / M6 Technische Universität München Boltzmannstrasse, 3 85748 Garching b. München, Germany
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Roche, Thomas. Uniqueness of a quasivariational sweeping process on functions of bounded variation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 363-394. http://archive.numdam.org/item/ASNSP_2012_5_11_2_363_0/

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