An Inverse Problem for Maxwell's Equations in Anisotropic Media*

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 ${\left( {\begin{array}{*{20}c} {{\varepsilon _{1} }} & {{\varepsilon _{2} }} \\ {{\varepsilon _{2} }} & {{\varepsilon _{3} }} \\ \end{array} } \right)}$ 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 ε₁, ε₂, ε₃, μ satisfy some a priori conditions.

Keywords

Anisotropic media / Inverse problem / Maxwell's equations / Carleman estimate / Lipschitz stability / 35R25 / 35R30 / 35Q60

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