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Non-convex sweeping processes in the space of regulated functions

  • *Corresponding author

    *Corresponding author

This work is dedicated to the memory of Jaroslav Kurzweil

Supported by the GAČR Grant No. 20-14736S, RVO: 67985840, and by the European Regional Development Fund, Project No. CZ.02.1.01/0.0/0.0/16_019/0000778. The third author is a member of GNAMPA-INdAM

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  • The aim of this paper is to study a wide class of non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i. e., functions of not necessarily bounded variation admitting one-sided limits at every point. Assuming that the time-dependent constraint is uniformly prox-regular and has uniformly non-empty interior, we prove existence and uniqueness of solutions, as well as continuous data dependence with respect to the sup-norm.

    Mathematics Subject Classification: 34G25, 34A60, 47J20, 49J52, 74C05.


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  • Figure 1.  Violation of the uniform non-empty interior condition

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