An inverse problem for Maxwell's equations in a uniaxially anisotropic medium

Inverse stable reconstruction of 3 coefficients for the heterogeneous Maxwell equations by finite number of partial interior observations

“…In [3], Bellassoued, Cristofol and Soccorsi gave a Hölder stability estimate for the determination of the dielectric permittivity and the magnetic permeability in heterogeneous Maxwell's equations by some partial boundary measurements, and in Beilina et al [2], the authors established a similar stability inequality using less observations and provide numerical simulations. Recently in Shang et al [19] the case of uniaxially anisotropic medium was addressed.…”

“…As for Maxwell's equations, we can refer to a standard textbook (pp. [16][17][18][19] in Jones [11] as just one example). Here the electric flux density D(x, t) and the magnetic flux density B(x, t) are three-dimensional vector-valued functions of the time t and the space variable x = (x 1 , x 2 , x 3 ).…”

Carleman estimates and some inverse problems for the coupled quantitative thermoacoustic equations by partial boundary layer data. Part II: Some inverse problems

“…For the development of this approach, there are many works. We refer to some of them (e.g., [7–38], and the references therein). The main advantages of this approach concern the finite number of observations required, the obtention of stability inequalities between the coefficient to be reconstructed, and the observation data.…”