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Determining the anisotropic traction state in a membrane by boundary measurements
A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media
1. | Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553 |
2. | INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France |
[1] |
Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems and Imaging, 2021, 15 (3) : 445-474. doi: 10.3934/ipi.2020075 |
[2] |
David Colton, Lassi Päivärinta, John Sylvester. The interior transmission problem. Inverse Problems and Imaging, 2007, 1 (1) : 13-28. doi: 10.3934/ipi.2007.1.13 |
[3] |
Kyoungsun Kim, Gen Nakamura, Mourad Sini. The Green function of the interior transmission problem and its applications. Inverse Problems and Imaging, 2012, 6 (3) : 487-521. doi: 10.3934/ipi.2012.6.487 |
[4] |
Fioralba Cakoni, Houssem Haddar, Isaac Harris. Homogenization of the transmission eigenvalue problem for periodic media and application to the inverse problem. Inverse Problems and Imaging, 2015, 9 (4) : 1025-1049. doi: 10.3934/ipi.2015.9.1025 |
[5] |
Yuebin Hao. Electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with a conductive boundary. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1387-1397. doi: 10.3934/cpaa.2020068 |
[6] |
Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems and Imaging, 2007, 1 (1) : 159-179. doi: 10.3934/ipi.2007.1.159 |
[7] |
Vesselin Petkov, Georgi Vodev. Localization of the interior transmission eigenvalues for a ball. Inverse Problems and Imaging, 2017, 11 (2) : 355-372. doi: 10.3934/ipi.2017017 |
[8] |
Luc Robbiano. Counting function for interior transmission eigenvalues. Mathematical Control and Related Fields, 2016, 6 (1) : 167-183. doi: 10.3934/mcrf.2016.6.167 |
[9] |
Qingjie Hu, Zhihao Ge, Yinnian He. Discontinuous Galerkin method for the Helmholtz transmission problem in two-level homogeneous media. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 2923-2948. doi: 10.3934/dcdsb.2020046 |
[10] |
Md. Ibrahim Kholil, Ziqi Sun. A uniqueness theorem for inverse problems in quasilinear anisotropic media. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022008 |
[11] |
Fioralba Cakoni, Anne Cossonnière, Houssem Haddar. Transmission eigenvalues for inhomogeneous media containing obstacles. Inverse Problems and Imaging, 2012, 6 (3) : 373-398. doi: 10.3934/ipi.2012.6.373 |
[12] |
Fioralba Cakoni, Shari Moskow, Scott Rome. The perturbation of transmission eigenvalues for inhomogeneous media in the presence of small penetrable inclusions. Inverse Problems and Imaging, 2015, 9 (3) : 725-748. doi: 10.3934/ipi.2015.9.725 |
[13] |
Fioralba Cakoni, Shari Moskow, Scott Rome. Asymptotic expansions of transmission eigenvalues for small perturbations of media with generally signed contrast. Inverse Problems and Imaging, 2018, 12 (4) : 971-992. doi: 10.3934/ipi.2018041 |
[14] |
Sergei Avdonin, Julian Edward. An inverse problem for quantum trees with observations at interior vertices. Networks and Heterogeneous Media, 2021, 16 (2) : 317-339. doi: 10.3934/nhm.2021008 |
[15] |
Fang Zeng, Pablo Suarez, Jiguang Sun. A decomposition method for an interior inverse scattering problem. Inverse Problems and Imaging, 2013, 7 (1) : 291-303. doi: 10.3934/ipi.2013.7.291 |
[16] |
Liping Wang, Juncheng Wei. Solutions with interior bubble and boundary layer for an elliptic problem. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 333-351. doi: 10.3934/dcds.2008.21.333 |
[17] |
Armin Lechleiter, Marcel Rennoch. Non-linear Tikhonov regularization in Banach spaces for inverse scattering from anisotropic penetrable media. Inverse Problems and Imaging, 2017, 11 (1) : 151-176. doi: 10.3934/ipi.2017008 |
[18] |
N. D. Alikakos, P. W. Bates, J. W. Cahn, P. C. Fife, G. Fusco, G. B. Tanoglu. Analysis of a corner layer problem in anisotropic interfaces. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 237-255. doi: 10.3934/dcdsb.2006.6.237 |
[19] |
Liping Wang, Dong Ye. Concentrating solutions for an anisotropic elliptic problem with large exponent. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3771-3797. doi: 10.3934/dcds.2015.35.3771 |
[20] |
Michele Di Cristo. Stability estimates in the inverse transmission scattering problem. Inverse Problems and Imaging, 2009, 3 (4) : 551-565. doi: 10.3934/ipi.2009.3.551 |
2020 Impact Factor: 1.639
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