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Hölder stability for an inverse medium problem with internal data

  • Mourad Choulli
  • Faouzi Triki
Research
  • 1 Downloads

Abstract

We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well posedness of the inversion in terms of the boundary conditions. We precisely show that we have actually a stability estimate of Hölder type. For sake of simplicity, we limited our study to the class of Helmholtz equations \(\Delta + V\) with bounded potential V.

Keywords

Helmholtz equation Inverse medium problem Internal data Hölder stability Unique continuation 

Mathematics Subject Classification

35R30 

Notes

Author's contributions

Acknowledgements

The authors were supported by the Grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.IECL, UMR CNRS 7502Université de LorraineMetz Cedex 01France
  2. 2.Laboratoire Jean Kuntzmann, UMR CNRS 5224Université Grenoble-AlpesSaint-Martin-d’HèresFrance

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