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Authors: Gebauer, Bastian
Hyvönen, Nuutti
Title: Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem
Online publication date: 19-Nov-2008
Language: english
Abstract: In various imaging problems the task is to use the Cauchy data of the solutions to an elliptic boundary value problem to reconstruct the coefficients of the corresponding partial differential equation. Often the examined object has known background properties but is contaminated by inhomogeneities that cause perturbations of the coefficient functions. The factorization method of Kirsch provides a tool for locating such inclusions. In this paper, the factorization technique is studied in the framework of coercive elliptic partial differential equations of the divergence type: Earlier it has been demonstrated that the factorization algorithm can reconstruct the support of a strictly positive (or negative) definite perturbation of the leading order coefficient, or if that remains unperturbed, the support of a strictly positive (or negative) perturbation of the zeroth order coefficient. In this work we show that these two types of inhomogeneities can, in fact, be located simultaneously. Unlike in the earlier articles on the factorization method, our inclusions may have disconnected complements and we also weaken some other a priori assumptions of the method. Our theoretical findings are complemented by two-dimensional numerical experiments that are presented in the framework of the diffusion approximation of optical tomography.
DDC: 510 Mathematik
510 Mathematics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
URN: urn:nbn:de:hebis:77-17976
Version: Accepted version
Publication type: Zeitschriftenaufsatz
License: In Copyright
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Journal: Inverse problems and imaging
Pages or article number: 355
Publisher: AIMS
Publisher place: Springfield, Mo.
Issue date: 2008
ISSN: 1930-8337
Appears in collections:JGU-Publikationen

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