BV solutions of rate independent differential inclusions

We consider a class of evolution differential inclusions defining the so called ``stop operator'', arising in elastoplasticity, ferromagnetism and phase transitions. These differential inclusions depend on a constraint which is represented by a convex set that is usually called ``characteristic set''. For BV data we compare different notions of BV solutions and we study how the continuity properties of the solution operators are related to the characteristic set. In the finite dimensional case we also give a geometric characterization of the cases when these kinds of solutions coincide for left-continuous inputs.