具有有界回缩的近端正则扫掠过程
Prox-regular sweeping processes with bounded retraction
AI总结：
本文证明了一致近端正则运动集驱动的 Moreau 扫掠过程在局部有界回缩条件下解的唯一性，并通过重参数化技术将该情形归结为可借助追赶算法求解的 Lipschitz 连续情形。
摘要：
本文的目的有两个方面。一方面，我们证明了由具有局部有界回缩的一致近端正则运动集驱动的 Moreau 扫掠过程具有唯一解，前提是近端正则系数大于驱动集的任何跳跃幅度。另一方面，我们展示了如何将局部有界回缩情形容易地归结为 $1$-Lipschitz 连续情形：实际上，我们首先借助所谓的“追赶算法”解决 Lipschitz 连续情形，然后通过对取值于近端正则集族的函数使用重参数化技术，将局部有界回缩情形归结为 Lipschitz 情形。
英文摘要：
The aim of this paper is twofold. On one hand we prove that the Moreau's sweeping process driven by a uniformly prox-regular moving set with local bounded retraction has a unique solution provided that the coefficient of prox-regularity is larger than the size of any jump of the driving set. On the other hand we show how the case of local bounded retraction can be easily reduced to the $1$-Lipschitz continuous case: indeed we first solve the Lipschitz continuous case by means of the so called ``catching-up algorithm", and we reduce the local bounded retraction case to the Lipschitz one by using a reparametrization technique for functions with values in the family of prox-regular sets.
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