Uniqueness of a quasivariational sweeping process on functions of bounded variation

作者：Roche Thomas^*

来源：Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 2012, 11(2): 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.

• 出版日期2012