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| In many hybrid imaging techniques the coefficients of a PDE have to be reconstructed from the knowledge of some internal measurements. In order to reconstruct the parameters, we need suitable boundary conditions (BCs) so that the corresponding solutions satisfy certain non-zero local constraints inside the domain. It is often easy to satisfy these constraints with the conductivity equation, but hard with other PDEs. The focus of this talk is to present an alternative strategy to the use of complex geometric optics solutions to find suitable BCs for frequency-dependent PDEs (conductivity equation with complex admittivity, Helmholtz equation or Maxwell's equations). In particular, I will show that if the non-zero constraints are satisfied for the conductivity equation with some BCs, then they are satisfied also for the other equations with the same BCs, provided that a finite number of frequencies, given a priori, are chosen in a fixed range. |
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