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

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