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A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation

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Abstract

This study provides a stability theory for the nonlinear least-squares formulation of estimating the diffusion coefficient in a two-point boundary-value problem from an error-corrupted observation of the state variable. It is based on analysing the projection of the observation on the nonconvex attainable set.

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Authors and Affiliations

  1. INRIA, Domaine de Voluceau-Rocquencourt, BP 105, 78153, Le Chesnay Cédex, France

    Guy Chavent

  2. CEREMADE, Université Paris Dauphine, 75775, Paris Cédex 16, France

    Guy Chavent

  3. Institut für Mathematik, Technical University of Graz, Kopernikusgasse 24, A-8010, Graz, Austria

    Karl Kunisch

Authors
  1. Guy Chavent
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  2. Karl Kunisch
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Additional information

Communicated by A. Bensoussan

This research was started while G. Chavent visited the Technical University of Graz. Support through the Steiermaerkische Landesregierung is gratefully acknowledged.

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Chavent, G., Kunisch, K. A geometric theory forL 2-stability of the inverse problem in a one-dimensional elliptic equation from anH 1-observation. Appl Math Optim 27, 231–260 (1993). https://doi.org/10.1007/BF01314817

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  • DOI: https://doi.org/10.1007/BF01314817

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