Multidimensional play operators with arbitrary BV inputs

TL;DR

This paper introduces an integral variational formulation for vector play operators with arbitrary BV inputs, proving existence and uniqueness, and connecting to existing formulations in special cases.

Contribution

It extends the theory of vector play operators to arbitrary BV inputs, providing a unified integral variational framework with proven uniqueness.

Findings

Unique solution existence for the new formulation.

Reduction to known cases in left and right continuous inputs.

Framework unifies different existing formulations.

Abstract

In this paper we provide an integral variational formulation for a vector play operator where the inputs are allowed to be arbitrary functions with (pointwise) bounded variation, not necessarily left or right continuous. We prove that this problem admits a unique solution, and we show that in the left continuous and right continuous cases it reduces to the well known existing formulations.