Abstract
In this paper we prove the existence and uniqueness of solutions of the following nonconvex variants of the sweeping process:
{-(u) over dot(t) is an element of N(C(t); (u) over dot(t))
u(0) = u(0) is an element of H, (u) over dot(0) is an element of C(0),
{-u(t) is an element of N(C(t); (u) over dot(t))
u(0) = u(0) is an element of H, (u) over dot(0) is an element of C(0),
where C : [0, T] paired right arrows H is a set valued mapping defined from [0, T] (T > 0) to a Hilbert space H and takes prox-regular values (not necessarily convex).