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BV prox-regular sweeping process with bounded truncated variation

ABSTRACT This paper is devoted to the existence and uniqueness of solutions for perturbed sweeping process measure differential inclusions in infinite dimensional setting. The possibly unbounded moving set is prox-regular and controlled only through the truncated Hausdorff-Pompeiu distance. The normal cone involved is perturbed by a kind of Carathéodory mapping satisfying a time-dependent hypomonotonicity assumption on bounded sets. Various properties of the solution mapping are also provided.