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November  2014, 8(4): 1117-1137. doi: 10.3934/ipi.2014.8.1117

## Calderón problem for Maxwell's equations in cylindrical domain

 1 Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784, United States 2 Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914

Received  December 2013 Revised  September 2014 Published  November 2014

We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations in a cylindrical domain $\Omega \times (0,L)$ from partial boundary map. More specifically, for an arbitrarily given subboundary $\Gamma_0 \subset \partial\Omega$, we prove that the coefficients of Maxwell's equations can be uniquely determined in the subdomain $(\Omega \setminus$ [the convex hull of $\Gamma_0])$ $\times (0,L)$ by the boundary map only for inputs vanishing on $\Gamma_0 \times (0,L)$.
Citation: Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems & Imaging, 2014, 8 (4) : 1117-1137. doi: 10.3934/ipi.2014.8.1117
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##### References:
 [1] Fabrice Delbary, Kim Knudsen. Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem. Inverse Problems & Imaging, 2014, 8 (4) : 991-1012. doi: 10.3934/ipi.2014.8.991 [2] Matteo Santacesaria. Note on Calderón's inverse problem for measurable conductivities. Inverse Problems & Imaging, 2019, 13 (1) : 149-157. doi: 10.3934/ipi.2019008 [3] Albert Clop, Daniel Faraco, Alberto Ruiz. Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities. Inverse Problems & Imaging, 2010, 4 (1) : 49-91. doi: 10.3934/ipi.2010.4.49 [4] Shumin Li, Masahiro Yamamoto, Bernadette Miara. A Carleman estimate for the linear shallow shell equation and an inverse source problem. Discrete & Continuous Dynamical Systems, 2009, 23 (1&2) : 367-380. doi: 10.3934/dcds.2009.23.367 [5] Lucie Baudouin, Emmanuelle Crépeau, Julie Valein. Global Carleman estimate on a network for the wave equation and application to an inverse problem. Mathematical Control & Related Fields, 2011, 1 (3) : 307-330. doi: 10.3934/mcrf.2011.1.307 [6] Petteri Piiroinen, Martin Simon. Probabilistic interpretation of the Calderón problem. Inverse Problems & Imaging, 2017, 11 (3) : 553-575. doi: 10.3934/ipi.2017026 [7] Pedro Caro, Mikko Salo. Stability of the Calderón problem in admissible geometries. Inverse Problems & Imaging, 2014, 8 (4) : 939-957. doi: 10.3934/ipi.2014.8.939 [8] Shitao Liu, Roberto Triggiani. Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness. Conference Publications, 2011, 2011 (Special) : 1001-1014. doi: 10.3934/proc.2011.2011.1001 [9] Daomin Cao, Ezzat S. Noussair, Shusen Yan. On the profile of solutions for an elliptic problem arising in nonlinear optics. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 649-666. doi: 10.3934/dcds.2004.11.649 [10] A. Doubov, Enrique Fernández-Cara, Manuel González-Burgos, J. H. Ortega. A geometric inverse problem for the Boussinesq system. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1213-1238. doi: 10.3934/dcdsb.2006.6.1213 [11] Andreas Kirsch. An integral equation approach and the interior transmission problem for Maxwell's equations. Inverse Problems & Imaging, 2007, 1 (1) : 159-179. doi: 10.3934/ipi.2007.1.159 [12] Aymen Jbalia. On a logarithmic stability estimate for an inverse heat conduction problem. Mathematical Control & Related Fields, 2019, 9 (2) : 277-287. doi: 10.3934/mcrf.2019014 [13] Yernat M. Assylbekov. Reconstruction in the partial data Calderón problem on admissible manifolds. Inverse Problems & Imaging, 2017, 11 (3) : 455-476. doi: 10.3934/ipi.2017021 [14] Sun-Sig Byun, Yunsoo Jang. Calderón-Zygmund estimate for homogenization of parabolic systems. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 6689-6714. doi: 10.3934/dcds.2016091 [15] Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 [16] Angkana Rüland, Eva Sincich. Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data. Inverse Problems & Imaging, 2019, 13 (5) : 1023-1044. doi: 10.3934/ipi.2019046 [17] María Ángeles García-Ferrero, Angkana Rüland, Wiktoria Zatoń. Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021049 [18] Lekbir Afraites, Chorouk Masnaoui, Mourad Nachaoui. Shape optimization method for an inverse geometric source problem and stability at critical shape. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021006 [19] Wenxiong Chen, Congming Li. A priori estimate for the Nirenberg problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 225-233. doi: 10.3934/dcdss.2008.1.225 [20] Chunpeng Wang, Yanan Zhou, Runmei Du, Qiang Liu. Carleman estimate for solutions to a degenerate convection-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4207-4222. doi: 10.3934/dcdsb.2018133

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