Realization of source conditions for linear ill-posed problems by conditional stability

• Main Authors: Hofmann, Bernd, Yamamoto, Masahiro
• Other Authors: TU Chemnitz, Fakultät für Mathematik
• Format: Others
• Language: English
• Published: Universitätsbibliothek Chemnitz 2008
• Subjects: Löwner's theorem; conditional stability; inverse PDE problems; linear ill-posed problems; operator monotonicity; regularization; source conditions; ddc:510; Inverser Operator; Inverses Problem
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800558; http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800558; http://www.qucosa.de/fileadmin/data/qucosa/documents/5575/data/t_06_ho_ya.pdf; http://www.qucosa.de/fileadmin/data/qucosa/documents/5575/20080055.txt

We prove some sufficient conditions for obtaining convergence rates in regularization of linear ill-posed problems in a Hilbert space setting and show that these conditions are directly related with the conditional stability in several concrete inverse problems for partial differential equations.