Continuity of the non-convex play operator in the space of rectifiable curves

TL;DR

This paper proves the continuity and rate independence of the non-convex play operator in the space of BV functions, with minimal assumptions on the constraint set, advancing understanding of its mathematical properties.

Contribution

It establishes the continuity of the non-convex play operator in BV spaces without requiring convexity of the constraint set, and proves its rate independence.

Findings

The non-convex play operator is continuous in BV-norm and BV-strict metrics.

The operator is rate independent regardless of the non-convexity of the constraints.

Continuity holds under minimal regularity assumptions on the constraint set.

Abstract

In this paper we prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the BV-norm and to the BV-strict metric in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.