Equicontinuous sweeping processes
Alexander Vladimirov
Discrete & Continuous Dynamical Systems - B 2013, 18(2): 565-573 doi: 10.3934/dcdsb.2013.18.565
We prove that the sweeping process on a "regular" class of convex sets is equicontinuous. Classes of polyhedral sets with a given finite set of normal vectors are regular, as well as classes of uniformly strictly convex sets. Regularity is invariant to certain operations on classes of convex sets such as intersection, finite union, arithmetic sum and affine transformation.
keywords: uniform continuity Sweeping process catching-up procedure.

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