Uniqueness of a quasivariational sweeping process on functions of bounded variation

• Thomas Roche ^[1]
  1. [1] Technical University Munich

     Technical University Munich

     Kreisfreie Stadt München, Alemania

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 11, Nº 2, 2012, págs. 363-394
• Idioma: inglés
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• Resumen

  • 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.