Yosida–Moreau Regularization of Sweeping Processes with Unbounded Variation

✍ Scribed by M. Kunze; M.D.P. Monteiro Marques

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 584 KB
• Volume: 130
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0144

✦ Synopsis

Let t [ C(t) be a Hausdorff-continuous multifunction with closed convex values in a Hilbert 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

a.e. on [0, T ], u * (0)=! 0 , are strongly pointwisely convergent as * Ä 0 + to the solution of the corresponding sweeping process, formally written as &du # N C(t) (u(t)), u(t) # C(t), u(0)=! 0 .