Mathematics > Analysis of PDEs
[Submitted on 29 Nov 2013 (v1), last revised 13 Jan 2015 (this version, v2)]
Title:On multiple frequency power density measurements II. The full Maxwell's equations
View PDFAbstract:We shall give conditions on the illuminations $\varphi_{i}$ such that the solutions to Maxwell's equations \[ \left\{ \begin{array}{l} {\rm curl} E^{i}=i\omega\mu H^{i}\qquad\text{in }\Omega,\\ {\rm curl} H^{i}=-i(\omega\varepsilon+i\sigma)E^{i}\qquad\text{in }\Omega,\\ E^{i}\times\nu=\varphi_{i}\times\nu\qquad\text{on }\partial\Omega, \end{array}\right. \] satisfy certain non-zero qualitative properties inside the domain $\Omega$, provided that a finite number of frequencies $\omega$ 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 [Inverse Problems 29 (2013) 115007], where the Helmholtz equation was studied.
Submission history
From: Giovanni S. Alberti [view email][v1] Fri, 29 Nov 2013 15:32:39 UTC (24 KB)
[v2] Tue, 13 Jan 2015 15:00:13 UTC (25 KB)
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