Non-convex sweeping processes in the space of regulated functions

0559099 - MÚ 2023 RIV US eng J - Journal Article
Krejčí, P. - Monteiro, Giselle Antunes - Recupero, V.
Non-convex sweeping processes in the space of regulated functions.
Communications on Pure and Applied Analysis. Roč. 21, č. 9 (2022), s. 2999-3029. ISSN 1534-0392. E-ISSN 1553-5258
R&D Projects: GA ČR(CZ) GA20-14736S
Institutional support: RVO:67985840
Keywords : evolution variational inequalities * sweeping processes * regulated functions
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Open access
http://dx.doi.org/10.3934/cpaa.2022087

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.
Permanent Link: https://hdl.handle.net/11104/0332518