REGULARITY OF PLATE EQUATIONS WITH CONTROL CONCENTRATED IN INTERIOR CURVES

We consider initial and boundary-value problems modelling the vibratio n of a plate with piezoelectric actuator. The usual models lead to the Bernoulli-Euler and Kirchhoff plate equations with right-hand side gi ven by a distribution concentrated in an interior curve. We obtain reg ularity results which are stronger than those obtained by simply using the Sobolev regularity of the right-hand side. By duality, we obtain new trace regularity properties for the solutions of plate equations. Our results provide appropriate function spaces for the control of pla tes provided with piezoelectric actuators.