Approximation from the exterior of a multifunction and its applications in the “sweeping process”

AbstractWe approximate from the exterior an upper semicontinuous multifunction C(·) from a metric space into the closed convex subsets of a normed space by means of globally Lipschitzean multifunctions; in particular, when C(·) is continuous, this approximation allows us to reduce the problem of the existence of solutions of the associated evolution equation to the case in which C(·) is Lipschitzean