BV-norm continuity of sweeping processes driven by a set with constant shape

TL;DR

This paper establishes the BV-norm well-posedness of sweeping processes driven by a convex set with constant shape, ensuring the BV-norm continuity of the play operator in elasto-plasticity models.

Contribution

It proves the BV-norm continuity and well-posedness of sweeping processes with a fixed-shape convex set, advancing the mathematical understanding of elasto-plasticity models.

Findings

Proved BV-norm well-posedness of the process

Established BV-norm continuity of the play operator

Enhanced mathematical framework for elasto-plasticity

Abstract

We prove the BV-norm well posedness of sweeping processes driven by a moving convex set with constant shape, namely the BV-norm continuity of the so-called play operator of elasto-plasticity.