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.

NON-CONVEX SWEEPING PROCESSES IN THE SPACE OF REGULATED FUNCTIONS / Krejci, P; Monteiro, Ga; Recupero, V. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 21:9(2022), pp. 2999-3029. [10.3934/cpaa.2022087]

NON-CONVEX SWEEPING PROCESSES IN THE SPACE OF REGULATED FUNCTIONS

Krejci, P;Recupero, V
2022

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2970826