We prove a logarithmic stability estimate for a parabolic inverse problem concerning the localization of unknown cavities in a thermic conducting medium Ω in ${\mathbb R}^n$, n ≥ 2, from a single pair of boundary measurements of temperature and thermal flux.

We consider solutions to the time-harmonic Maxwell's Equationsof a TE (transverse electric) nature. For such solutions we providea rigorous derivation of the leading order boundary perturbationsresulting from the presence of a finite number of interior inhomogeneitiesof small diameter. We expect that these formulas will form the basis for very effective computational identification algorithms, aimed at determininginformation about the inhomogeneities from electromagnetic boundary measurements.