The play operator on the rectifiable curves in a Hilbert space

The vector play operator is the solution operator of a class of evolution variational inequalities arising in continuum mechanics. For regular data the existence of solutions is easily obtained from general results from the theory of maximal monotone operators. If the datum is assumed to be a continuous function of bounded variation, then the existence of a weak solution is usually proved by means of a time discretization procedure. In this paper we give a short proof of the existence of the play operator on the space of rectifiable curves making use of basic facts of measure theory. We also drop the separability assumptions usually made by other authors.