Hölder stability for an inverse medium problem with internal data

  • Mourad Choulli
  • Faouzi TrikiEmail author


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.


Helmholtz equation Inverse medium problem Internal data Hölder stability Unique continuation 

Mathematics Subject Classification



Author's contributions


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


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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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