Abstract
Several papers have been recently devoted to properties of prox-regular (or proximally smooth) nonconvex sets in Hilbert spaces. Motivated by the study of differential inclusions defined by nonconvex sweeping process, we establish new characterizations of prox-regular sets S in terms of the subdifferential of the distance function d(s) associated with S. Using these characterizations we prove an existence result of the perturbed nonconvex sweeping process in Hilbert space.