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

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