Explicit characterization of the support of non-linear inclusions

Armin Lechleiter

doi:10.3934/ipi.2011.5.675

Article Contents

2011, Volume 5, Issue 3: 675-694. Doi: 10.3934/ipi.2011.5.675

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Explicit characterization of the support of non-linear inclusions

Armin Lechleiter^1,

1.
INRIA Saclay–Ile-de-France and CMAP, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex

Received: September 2010

Revised: June 2011

Published: August 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 35R30, 31B20, 78A46; Secondary: 45Q05.

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