Regularity Of Plate Equations With Control Concentrated In Interior Curves

. We consider initial and boundary value problems modelling the vibration of a plate with piezoelectric actuator. The usual models lead to the Bernoulli-Euler and Kirchhoff plate equations with right hand side given by a distribution concentrated in an interior curve. We obtain regularity 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 equation. Our results provide appropriate function spaces for the control of plates provided with piezoelectric actuators. 1. Introduction The aim of this paper is to study regularity of solutions for plate equations with control given by the normal derivative of the Dirac mass concentrated in a curve. Our motivation comes from recent work on modelling, analysis and control of elastic structures provided with piezoelectric actuators (see [?], [?], [?], [?]). In [?] and [?] the authors give the well-posedness resul..