Abstract
Physically, the conductivity equation is obtained as a low-frequency limit of time-harmonic Maxwell's equations. In this work we consider the relation of corresponding inverse boundary value problems. The behaviour of the impedance mapping for time-harmonic Maxwell's equations is analysed when the frequency goes to zero where Maxwell's equations have an eigenvalue of infinite multiplicity. We show that an appropriate restriction of the impedance mapping for Maxwell's equations has a low-frequency limit. Also, we give a formula from which the impedance imaging data (the Dirichlet-to-Neumann mapping for the conductivity equation) can be calculated by using the low-frequency limit of the impedance mapping.
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