Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress

We derive weak Carleman estimates with two large parameters for a general partial dierential operator of second order under pseudo-convexity conditions on the weight function. We use these estimates to derive most nat- ural Carleman type estimates for the (anisotropic) system of elasticity with residual stress and give applications to uniqueness and stability of the contin- uation and identication of the residual stress from boundary measurements. We give explicit sucient pseudo-convexity conditions. Proofs use dierential quadratic forms and Fourier analysis, combined with special (micro)localization arguments.