Authors:	Gebauer, Bastian
Title:	The factorization method for real elliptic problems
Online publication date:	12-Nov-2008
Year of first publication:	2006
Language:	english
Abstract:	The Factorization Method localizes inclusions inside a body from measurements on its surface. Without a priori knowing the physical parameters inside the inclusions, the points belonging to them can be characterized using the range of an auxiliary operator. The method relies on a range characterization that relates the range of the auxiliary operator to the measurements and is only known for very particular applications. In this work we develop a general framework for the method by considering symmetric and coercive operators between abstract Hilbert spaces. We show that the important range characterization holds if the difference between the inclusions and the background medium satisfies a coerciveness condition which can immediately be translated into a condition on the coefficients of a given real elliptic problem. We demonstrate how several known applications of the Factorization Method are covered by our general results and deduce the range characterization for a new example in linear elasticity.
DDC:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-308
URN:	urn:nbn:de:hebis:77-17704
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	In Copyright
Information on rights of use:	https://rightsstatements.org/vocab/InC/1.0/
Journal:	Zeitschrift für Analysis und ihre Anwendungen 25
Pages or article number:	81 102
Issue date:	2006
ISSN:	0232-2064
Appears in collections:	JGU-Publikationen