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May  2010, 27(2): 799-825. doi: 10.3934/dcds.2010.27.799

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

Victor Isakov 1, and  Nanhee Kim 2,

1. 

Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260, United States
2. 

Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67206, United States

Received  October 2009 Revised  February 2010 Published  February 2010

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.
Keywords: Elasticity system with residual stress., Carleman estimates.
Mathematics Subject Classification: Primary: 35R30; Secondary: 35L3.
Citation: Victor Isakov, Nanhee Kim. Weak Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 799-825. doi: 10.3934/dcds.2010.27.799
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