Sweeping by a continuous prox-regular set

The evolution problem known as sweeping process is considered for a class of nonconvex sets called prox-regular (or -convex). Assuming, essentially, that such sets contain in the interior a suitable subset and move continuously (w.r.t. the Hausdorff distance), we prove local and global existence as well as uniqueness of solutions, which are continuous functions with bounded variation. Some examples are presented