A uniqueness result for the linear system of elasticity and its control theoretical consequences (vol 34, pg 1473, 1996)

In this note we explain why the three-dimensional counterexample of section 7.2 of the paper under consideration [E. Zuazua, SIAM J. Control Optim., 3 4 (1996), pp. 1473-1495] is incorrect. It concerns the existence of eigenfu nctions for the Dirichlet Laplacian of a special form. We claimed the exist ence of particular three-dimensional domains in which these eigenfunctions do exist. However, in a recent joint work with G. Sweers [G. Sweers and E. Zuazua, J. Elasticity, to appear], we have proved that they may not exist i n any bounded Lipschitz domain in dimensions n greater than or equal to 3.