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| An Inverse Problem for Maxwell’s Equations in Anisotropic Media |
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Citation： |
Shumin LI,Masahiro YAMAMOTO.An Inverse Problem for Maxwell’s Equations in Anisotropic Media[J].Chinese Annals of Mathematics B,2007,28(1):35~54 |
| Page view： 1304
Net amount： 1064 |
Authors： |
Shumin LI; Masahiro YAMAMOTO |
Foundation： |
Project supported by the Rotary Yoneyama Doctor Course Scholarship (Japan), the Fujyu-kai (Tokyo, Japan), the 21st Century Center of Excellence Program at Graduate School of Mathematical Sciences, the University of Tokyo, the Japan Society for the Promotion of Science (No. 15340027) and the Ministry of Education, Cultures, Sports and Technology (No. 17654019). |
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| Abstract： |
The authors consider Maxwell’s equations for an isomagnetic anisotropic and inhomogeneous medium in two dimensions, and discuss an inverse problem of determining the permittivity tensor $\big(\begin{smallmatrix}\varepsilon_1 & \varepsilon_2\\ \varepsilon_2 & \varepsilon_3\end{smallmatrix}\big)$ and the permeability μ in the constitutive relations from a finite number of lateral boundary measurements. Applying a Carleman estimate, the authors prove an estimate of the Lipschitz type for stability, provided that $\varepsilon_1$, $\varepsilon_2$, $\varepsilon_3$, μ satisfy some a priori conditions. |
Keywords： |
Anisotropic media, Inverse problem, Maxwell’s equations, Carleman estimate, Lipschitz stability |
Classification： |
35R25, 35R30, 35Q60 |
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