VOSIDA-MOREAU REGULARIZATION OF SWEEPING PROCESSES WITH UNBOUNDED VARIATION

Let t --> C(t) be a Hausdorff-continuous multifunction with closed con vex values in a Hilbert space H such that C(t) has nonempty interior f or all t. We show that the Yosida-Moreau regularizations of the sweepi ng process with moving set C(t), i.e., the solutions of du(lambda)/dt( t) + 1/lambda [u(lambda)(t) - proj(u(lambda)(t), C(t))] = 0 a.e. on [0 , T], u(lambda)(0) = xi(0), are strongly pointwisely convergent as lam bda --> 0(+) to the solution of the corresponding sweeping process, fo rmally written as -du is an element of N-C(t)(u(t)), u(t) is an elemen t of C(t), u(0) = xi(0). (C) 1996 Academic Press, Inc.