A noncontrollability result for systems of mixed order

In this paper we prove an abstract theorem of noncontrollability for the ev olution equation associated to a Douglis-Nirenberg elliptic system of mixed order with nonempty essential spectrum. In particular, we show by Weyl's c haracterization of the essential spectrum that the condition of exact contr ollability does not hold true. We discuss examples concerning the elasticit y operator in the framework of the linear membrane shell theory.