THE IMPEDANCE IMAGING PROBLEM AS A LOW-FREQUENCY LIMIT

Physically, the conductivity equation is obtained as a low-frequency l imit of time-harmonic Maxwell's equations. In this work we consider th e relation of corresponding inverse boundary value problems. The behav iour of the impedance mapping for time-harmonic Maxwell's equations is analysed when the frequency goes to zero where Maxwell's equations ha ve an eigenvalue of infinite multiplicity. We show that an appropriate restriction of the impedance mapping for Maxwell's equations has a lo w-frequency limit. Also, we give a formula from which the impedance im aging data (the Dirichlet-to-Neumann mapping for the conductivity equa tion) can be calculated by using the low-frequency limit of the impeda nce mapping.