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Some Geometric Inverse Problems for the Lamé System with Applications in Elastography

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Abstract

In this paper, we consider some geometric inverse problems for the Lamé system. A first motivation comes from from elastography, a technique that allows to identify the elastic properties of tissues and can serve, among other things, to detect a tumor from non-invasive (external) measurements. A second one is to identify a rigid structure in an elastic medium. We prove a uniqueness result, we introduce some iterative methods for the reconstruction problem and we present the results of several numerical experiments.

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Authors and Affiliations

  1. University of Sevilla, Dpto. E.D.A.N. and I.M.U.S., Aptdo. 1160, 41080, Sevilla, Spain

    Anna Doubova & Enrique Fernández-Cara

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  1. Anna Doubova
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  2. Enrique Fernández-Cara
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Correspondence to Anna Doubova.

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Partially supported by Grant MTM2016-76990-P.

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Doubova, A., Fernández-Cara, E. Some Geometric Inverse Problems for the Lamé System with Applications in Elastography. Appl Math Optim 82, 1–21 (2020). https://doi.org/10.1007/s00245-018-9487-8

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