Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. II: The full Maxwell equations.

DOI10.1016/S0021-7824(01)01217-XzbMath1042.78002MaRDI QIDQ1606251

Michael S. Vogelius, Habib Ammari, Darko Volkov

Publication date: 24 July 2002

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

Maxwell equationsasymptotic formulasboundary perturbationssmall inhomogeneities

Mathematics Subject Classification ID

Electromagnetic theory (general) (78A25) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Asymptotic analysis in optics and electromagnetic theory (78M35)

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Cites Work

• Unnamed Item
• Unnamed Item
• Nondestructive evaluation of plates using eddy current methods
• An inverse boundary value problem in electrodynamics
• Total determination of material parameters from electromagnetic boundary information
• Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients
• Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence
• Structure of the set of stationary solutions of the navier‐stokes equations
• Applications of analysis on nilpotent groups to partial differential equations
• Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction
• Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
• Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter
• A Finite Element/Spectral Method for Approximating the Time-Harmonic Maxwell System in $\mathbb{R}^3 $
• The layer potential technique for the inverse conductivity problem
• Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area