Carleman estimate for a stationary isotropic Lamé system and the applications |
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Authors: | Oleg Yu Imanuvilov Masahiro Yamamoto † |
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Institution: | 1. Department of Mathematics , 400 Carver Hall, Iowa State University , Ames IA 50011-2064, USA;2. Department of Mathematical Sciences , The University of Tokyo , 3-8-1 Komaba, Meguro, Tokyo 153, Japan |
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Abstract: | For the isotropic stationary Lamé system with variable coefficients equipped with the Dirichlet or surface stress boundary condition, we obtain a Carleman estimate such that (i) the right hand side is estimated in a weighted L 2-space and (ii) the estimate includes nonhomogeneous surface displacement or surface stress. Using this estimate we establish the conditional stability in Sobolev's norm of the displacement by means of measurements in an arbitrary subdomain or measurements of surface displacement and stress on an arbitrary subboundary. Finally by the Carleman estimate, we prove the uniqueness and conditional stability for an inverse problem of determining a source term by a single interior measurement. |
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Keywords: | Lamé system Carleman estimate Unique continuation Inverse source problem 1991 Mathematics Subject Classifications: 35B60 35R30 74B05 |
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