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.

中文翻译：

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绝对连续函数空间中的显式和隐式非凸扫描过程

我们表明，可能具有非凸正则约束的扫描过程在绝对连续函数的空间中生成强连续的输入-输出映射。在约束的额外平滑假设下，我们证明了输入-输出映射的局部 Lipschitz 连续性。使用 Banach 收缩原理，我们随后证明了与状态相关问题相关的解映射也是局部 Lipschitz 连续的。