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Inverse Problems in Science and Engineering Volume 29, 2021 - Issue 3
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Research Article

Lipschitz stability estimate and reconstruction of Lamé parameters in linear elasticity

S. Eberlea Institute of Mathematics, Goethe-University Frankfurt, Frankfurt am Main, GermanyCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-4243-3643
ORCID Icon,
B. Harracha Institute of Mathematics, Goethe-University Frankfurt, Frankfurt am Main, GermanyORCID Iconhttps://orcid.org/0000-0002-8666-7791
ORCID Icon,
H. Meftahib ENIT of Tunisia, Tunis, Tunisia
&
T. Rezguib ENIT of Tunisia, Tunis, Tunisia
Pages 396-417 | Received 05 Jun 2019, Accepted 01 Jul 2020, Published online: 27 Jul 2020

Citations (14)

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H. Meftahi & A. Potschka. (2023) Elastic shear modulus and density profiles inversion: Lipschitz stability results. Applicable Analysis 0:0, pages 1-16.
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Articles from other publishers (13)

Sonia Foschiatti. (2024) Lipschitz stability estimate for the simultaneous recovery of two coefficients in the anisotropic Schrödinger type equation via local Cauchy data. Journal of Mathematical Analysis and Applications 531:1, pages 127753.
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Tian Xu, Zhen Wang, Yingda Hu, Shilun Du & Yong Lei. (2023) A multiple-data-based direct method for inverse problem in three-dimensional linear elasticity. International Journal of Mechanical Sciences 259, pages 108600.
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Sarah Eberle-Blick & Bastian Harrach. (2023) Resolution guarantees for the reconstruction of inclusions in linear elasticity based on monotonicity methods. Inverse Problems 39:7, pages 075006.
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Vanessa Markaki, Drosos Kourounis & Antonios Charalambopoulos. (2023) On the identification of Lamé parameters in linear isotropic elasticity via a weighted self-guided TV-regularization method. Journal of Inverse and Ill-posed Problems 0:0.
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Giovanni S Alberti, Ángel Arroyo & Matteo Santacesaria. (2022) Inverse problems on low-dimensional manifolds. Nonlinearity 36:1, pages 734-808.
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Tian Xu, Zhen Wang, Yingda Hu, Shilun Du, Ao Du, Zhenyang Yu & Yong Lei. (2023) A FEM-based direct method for identification of Young’s modulus and boundary conditions in three-dimensional linear elasticity from local observation. International Journal of Mechanical Sciences 237, pages 107797.
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Andrea Aspri. (2022) A phase-field approach for detecting cavities via a Kohn–Vogelius type functional. Inverse Problems 38:9, pages 094001.
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Sarah Eberle & Bastian Harrach. (2022) Monotonicity-based regularization for shape reconstruction in linear elasticity. Computational Mechanics 69:5, pages 1069-1086.
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Sarah Eberle & Jochen Moll. (2021) Experimental detection and shape reconstruction of inclusions in elastic bodies via a monotonicity method. International Journal of Solids and Structures 233, pages 111169.
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Antonio Corbo Esposito, Luisa Faella, Gianpaolo Piscitelli, Ravi Prakash & Antonello Tamburrino. (2021) Monotonicity Principle in tomography of nonlinear conducting materials * . Inverse Problems 37:4, pages 045012.
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Sarah Eberle & Bastian Harrach. (2021) Shape reconstruction in linear elasticity: standard and linearized monotonicity method. Inverse Problems 37:4, pages 045006.
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Houcine Meftahi. (2021) Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem. SIAM Journal on Mathematical Analysis 53:6, pages 6326-6354.
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Bastian Harrach. (2020) Uniqueness, stability and global convergence for a discrete inverse elliptic Robin transmission problem. Numerische Mathematik 147:1, pages 29-70.
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