Non-convex sweeping processes in the space of regulated functions

Pavel Krejčí; Giselle Antunes Monteiro; Vincenzo Recupero

doi:10.3934/cpaa.2022087

Article Contents

2022, Volume 21, Issue 9: 2999-3029. Doi: 10.3934/cpaa.2022087

This issue Previous Article Plateau-rayleigh instability of singular minimal surfaces Next Article Strongly singular convective elliptic equations in

$ \mathbb{R}^N $

driven by a non-homogeneous operator

Non-convex sweeping processes in the space of regulated functions

1.
Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 16629 Praha 6, Czech Republic
2.
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic
3.
Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

^*Corresponding author
^*Corresponding author

This work is dedicated to the memory of Jaroslav Kurzweil

Received: October 31, 2021

Revised: March 31, 2022

Early access: May 2022

Published: September 2022

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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Abstract

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.

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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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