Non-convex sweeping processes in the space of regulated functions

TL;DR

This paper investigates a broad class of non-convex sweeping processes with moving constraints modeled by regulated functions, establishing existence, uniqueness, and stability of solutions under certain regularity conditions.

Contribution

It introduces a framework for analyzing non-convex sweeping processes with regulated functions, proving key properties like existence and uniqueness of solutions.

Findings

Existence and uniqueness of solutions are proven.

Solutions depend continuously on initial data.

The framework applies to non-convex, moving constraints modeled by regulated functions.

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.