Yosida-Moreau regularization of sweeping processes with unbounded variation

Abstract

Let t → C(t) be a Hausdorff-continuous multifunction with closed convex values in a Hubert space H such that C(t) has nonempty interior for all t. We show that the Yosida-Moreau regularizations of the sweeping process with moving set C(t), i.e., the solutions of duλ/dt (t) +1/λ [uλ(t) - proj(uλ(t), C(t))] = 0 a.e. on [0, T], uλ(0) = ξ0, are strongly pointwisely convergent as λ → 01 to the solution of the corresponding sweeping process, formally written as - du ∈ N C(t)(u(t)), u(t) ∈ C(t), u(0) = ξ0. © 1996 Academic Press, Inc.