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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.

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