BV solutions of nonconvex sweeping process differential inclusion with perturbation

Abstract

This paper is devoted to the study of differential inclusions, particularly discontinuous perturbed sweeping processes in the infinite-dimensional setting. On the one hand, the sets involved are assumed to be prox-regular and to have a variation given by a function which is of bounded variation and right continuous. On the other hand, the perturbation satisfies a linear growth condition with respect to a fixed compact subset. Finally, the case where the sets move in an absolutely continuous way is recovered as a consequence.