On multiple frequency power density measurements II. The full Maxwell's equations

• Published in: Journal of Differential Equations Vol. 258; no. 8; pp. 2767 - 2793
• Main Author: Alberti, Giovanni S.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.04.2015
• Subjects: Hybrid imaging; Internal measurements; Maxwell's equations; Multiple frequencies; Qualitative properties; Sets of measurements; Internal measurements; Sets of measurements; 35R30; Hybrid imaging; 35B30; Maxwell's equations; Qualitative properties; Multiple frequencies; 35Q61
• ISSN: 0022-0396; 1090-2732
• DOI: 10.1016/j.jde.2014.12.028

We shall give conditions on the illuminations φi such that the solutions to Maxwell's equations{curlEi=iωμHiin Ω,curlHi=−i(ωε+iσ)Eiin Ω,Ei×ν=φi×νon ∂Ω, satisfy certain non-zero qualitative properties inside the domain Ω, provided that a finite number of frequencies ω are chosen in a fixed range. The illuminations are explicitly constructed. This theory finds applications in several hybrid imaging problems, where unknown parameters have to be imaged from internal measurements. Some of these examples are discussed. This paper naturally extends a previous work of the author (2013) [7], where the Helmholtz equation was studied.