Non-convex sweeping processes in the space of regulated functions
Pavel Krejčı́, Giselle Antunes Monteiro, Vincenzo Recupero · Communications on Pure & Applied Analysis · 2022
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.