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.
@article{ASNSP_2012_5_11_2_363_0, author = {Roche, Thomas}, title = {Uniqueness of a quasivariational sweeping process on functions of bounded variation}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {363--394}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {2}, year = {2012}, zbl = {1250.49012}, mrnumber = {3011995}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2012_5_11_2_363_0/} }
TY - JOUR AU - Roche, Thomas TI - Uniqueness of a quasivariational sweeping process on functions of bounded variation JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 363 EP - 394 VL - 11 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2012_5_11_2_363_0/ LA - en ID - ASNSP_2012_5_11_2_363_0 ER -
%0 Journal Article %A Roche, Thomas %T Uniqueness of a quasivariational sweeping process on functions of bounded variation %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 363-394 %V 11 %N 2 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2012_5_11_2_363_0/ %G en %F ASNSP_2012_5_11_2_363_0
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://www.numdam.org/item/ASNSP_2012_5_11_2_363_0/
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