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Explicit characterization of the support of non-linear inclusions

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  • We study inverse problems for non-linear penetrable media in the context of scattering theory and impedance tomography. Using a general description of the range of the non-linear far-field operator we show an explicit characterization of the support of a weakly non-linear inhomogeneous scattering object. Application of the same technique to the impedance tomography problem for a monotonic non-linear inclusion yields a characterization of the inclusion's support from the non-linear Neumann-to-Dirichlet operator.
    Mathematics Subject Classification: Primary: 35R30, 31B20, 78A46; Secondary: 45Q05.


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