The focus of this paper is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capability of our method is illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-72654 |
| Date | 06 September 2011 |
| Creators | Tautenhahn, Ulrich, Hämarik, Uno, Hofmann, Bernd, Shao, Yuanyuan |
| Contributors | Technische Universität Chemnitz, Fakultät für Mathematik, Hochschule Zittau/Görlitz, Fak. für Mathematik und Naturwissenschaften, Universität Tartu - Estonia, Institut für Mathematik, Technische Universität Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, text/plain, application/zip |
| Relation | dcterms:isPartOf:Preprintreihe der Fakultät für Mathematik der TU Chemnitz ; 2011-16 |
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