Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin of the South Ural State University Année : 2015

Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map

Résumé

We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schrödinger equation in a bounded domain, from a partial elliptic Dirichlet-to-Neumann map. Namely, the Dirichlet data is imposed on the shadowed face of the boundary of the domain and the Neumann data is measured on its illuminated face. We establish a log log stability estimate for the L 2 -norm (resp. the H −1 -norm) of H t , for t > 0, and bounded (resp. L 2) potentials.
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Dates et versions

hal-01096168 , version 1 (16-12-2014)

Identifiants

  • HAL Id : hal-01096168 , version 1

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Mourad Choulli, Yavar Kian, Eric Soccorsi. Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map. Bulletin of the South Ural State University, 2015, 8 (3), pp.78-94. ⟨hal-01096168⟩
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