Double Logarithmic Stability in the Identification of a Scalar Potential by a Partial Elliptic Dirichlet-to-Neumann Map | Zendy

Mourad Choulli | Zendy; Yavar Kian | Zendy; Éric Soccorsi | Zendy

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Double Logarithmic Stability in the Identification of a Scalar Potential by a Partial Elliptic Dirichlet-to-Neumann Map

Author(s) -

Mourad Choulli,

Yavar Kian,

Éric Soccorsi

Publication year - 2015

Publication title -

bulletin of the south ural state university series mathematical modelling programming and computer software

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.338

H-Index - 11

eISSN - 2308-0256

pISSN - 2071-0216

DOI - 10.14529/mmp150305

Subject(s) - bounded function , neumann boundary condition , mathematics , dirichlet distribution , scalar (mathematics) , norm (philosophy) , logarithm , mathematical analysis , elliptic curve , domain (mathematical analysis) , boundary value problem , pure mathematics , geometry , political science , law

We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schr{\"o}dinger 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 L2-norm (resp. the H minus 1-norm) of bounded (resp. L2) potentials whose difference is lying in any Sobolev space of order positive order.

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