Geodesic
Uniqueness of a quasivariational sweeping process on functions of bounded variation
Roche, Thomas1
1 Department of Mathematics / M6 Technische Universität München Boltzmannstrasse, 3 85748 Garching b. München, Germany
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 363-394

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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.

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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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     title = {Uniqueness of a quasivariational sweeping process on functions of bounded variation},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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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, Série 5, Tome 11 (2012) no. 2, pp. 363-394. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_2_363_0/