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

Abstract

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