The Sweeping Processes without Convexity
- Cite this article as:
- Colombo, G. & Goncharov, V.V. Set-Valued Analysis (1999) 7: 357. doi:10.1023/A:1008774529556
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We study the sweeping processes in a Hilbert space which are generated by a closed not necessarily convex moving set. A technique is developed, based on measurability properties of normal cones, in order to prove existence of solutions. Some existence results are proved, with or without hypothesis of compactness; moreover, under suitable assumptions, uniqueness and regularity properties are established. In particular, the well-known results of Moreau are extended to a class of not necessarily convex (called ϕ-convex) sets.