### A remark on the local Lipschitz continuity of vector hysteresis operators

It is known that the vector stop operator with a convex closed characteristic $Z$ of class ${C}^{1}$ is locally Lipschitz continuous in the space of absolutely continuous functions if the unit outward normal mapping $n$ is Lipschitz continuous on the boundary $\partial Z$ of $Z$. We prove that in the regular case, this condition is also necessary.