Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters

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The method of equation error can be posed and analyzed in an abstract setting that encompasses a variety of elliptic inverse problems, in which a coefficient in an elliptic partial differential equation is to be estimated from a measurement of the solution to a boundary value problem. Stability in the presence of measurement error is obtained by regularization, and since the abstract setting admits the use of total variation regularization, rapidly varying or even discontinuous coefficients can be estimated. The proposed method effectively identifies Lamé' parameters in the system of linear isotropic elasticity.

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Publisher's version of record: https://doi.org/10.1080/17415970701602580

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Inverse Problems in Science and Engineering