Carleman Estimates with Second Large Parameter for Second Order Operators

Abstract

In this paper we prove Carleman type estimates with two large parameters for general linear partial differential operators of second order. By using second large parameter we derive from results for scalar equations first Carleman estimates for dynamical Lame system with residual stress. We apply these estimates to obtain a Holder and Lipschitz stability estimates of continuation of solutions of this system under some pseudo-convexity assumptions. So we obtain first uniqueness and stability of the continuation results for an important anisotropic system of elasticity without assumption that this system is close to an isotropic system.