Ellipticity Loss in Isotropic Elasticity

In this paper we prove that the equilibrium displacement of an isotropic elastic solid under imposed boundary displacement converges in the strong H1 topology when the shear modulus goes to zero. As a consequence, we show that the dependence on material constants may be dropped in the classical inequality expressing the continuous dependence of elastic equilibria on the boundary displacement. This revised version was published online in August 2006 with corrections to the Cover Date.