Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem

dc.contributor.authorGebauer, Bastian
dc.contributor.authorHyvönen, Nuutti
dc.date.accessioned2008-11-19T14:14:48Z
dc.date.available2008-11-19T15:14:48Z
dc.date.issued2008
dc.description.abstractIn 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.en_GB
dc.identifier.doihttp://doi.org/10.25358/openscience-314
dc.identifier.urihttps://openscience.ub.uni-mainz.de/handle/20.500.12030/316
dc.identifier.urnurn:nbn:de:hebis:77-17976
dc.language.isoeng
dc.rightsInC-1.0de_DE
dc.rights.urihttps://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematikde_DE
dc.subject.ddc510 Mathematicsen_GB
dc.titleFactorization method and inclusions of mixed type in an inverse elliptic boundary value problemen_GB
dc.typeZeitschriftenaufsatzde_DE
jgu.journal.issue3
jgu.journal.titleInverse problems and imaging
jgu.journal.volume2
jgu.organisation.departmentFB 08 Physik, Mathematik u. Informatik
jgu.organisation.nameJohannes Gutenberg-Universität Mainz
jgu.organisation.number7940
jgu.organisation.placeMainz
jgu.organisation.rorhttps://ror.org/023b0x485
jgu.pages.end372
jgu.pages.start355
jgu.publisher.issn1930-8337
jgu.publisher.nameAIMS
jgu.publisher.placeSpringfield, Mo.
jgu.publisher.year2008
jgu.rights.accessrightsopenAccess
jgu.subject.ddccode510
jgu.type.dinitypeArticle
jgu.type.resourceText
jgu.type.versionAccepted versionen_GB
opus.affiliatedGebauer, Bastian
opus.date.accessioned2008-11-19T14:14:48Z
opus.date.available2008-11-19T15:14:48
opus.date.modified2008-11-25T08:43:27Z
opus.identifier.opusid1797
opus.institute.number0804
opus.metadataonlyfalse
opus.organisation.stringFB 08: Physik, Mathematik und Informatik: Institut für Mathematikde_DE
opus.subject.dfgcode00-000
opus.subject.otherFactorization method, inverse elliptic boundary value problems, inclusionsen_GB
opus.type.contenttypeKeinede_DE
opus.type.contenttypeNoneen_GB

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