We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output mapping. Using the Banach contraction principle, we subsequently prove that also the solution mapping associated with the state-dependent problem is locally Lipschitz continuous.

Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions / Krejci, Pavel; Giselle Antunes Monteiro, ; Recupero, Vincenzo. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - STAMPA. - 84:Supplement issue 2(2021), pp. 1477-1504. [10.1007/s00245-021-09801-8]

Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions

Pavel Krejci;recupero
2021

Abstract

We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output mapping. Using the Banach contraction principle, we subsequently prove that also the solution mapping associated with the state-dependent problem is locally Lipschitz continuous.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2909732