Ulrich Tautenhahn, Uno Hämarik, Bernd Hofmann, Yuanyuan Shao: Conditional stability estimates for ill-posed PDE problems by using interpolation

Author(s):

Ulrich Tautenhahn
Uno Hämarik
Bernd Hofmann
Yuanyuan Shao

Title:

Conditional stability estimates for ill-posed PDE problems by using interpolation

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 16, 2011

Mathematics Subject Classification:

35R25	[]
35R30	[]
65J20	[]
65J22	[]
65M30	[]
65M32	[]

Abstract:

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.

Keywords:

Ill-posed problems, inverse problems, conditional stability estimates, interpolation, elliptic problems, parabolic problems, source problems, analytic continuation

Language:

English

Publication time:

07/2011