Set-Valued Analysis

, Volume 7, Issue 4, pp 357–374

The Sweeping Processes without Convexity

  • Giovanni Colombo
  • Vladimir V. Goncharov

DOI: 10.1023/A:1008774529556

Cite this article as:
Colombo, G. & Goncharov, V.V. Set-Valued Analysis (1999) 7: 357. doi:10.1023/A:1008774529556


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.

evolution inclusions normal cones Scorza–Dragoni property 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Giovanni Colombo
    • 1
  • Vladimir V. Goncharov
    • 2
  1. 1.Dipartimento di Matematica Pura e ApplicataUniversità di PadovaPadovaItaly
  2. 2.SISSATriesteItaly

Personalised recommendations