论文标题
在绝对连续功能的空间中的显式和隐式非凸扫过程
Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions
论文作者
论文摘要
我们表明，具有非Convex Prox-Regular约束的扫描过程在绝对连续函数的空间中生成了强烈的连续输入输出映射。在约束上的其他平滑度假设下，我们证明了输入输出映射的本地Lipschitz连续性。使用BANACH收缩原则，我们随后证明与国家依赖性问题相关的解决方案映射是局部Lipschitz的连续。
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.
