Geodesic
Double logarithmic stability in the identification of a scalar potential by~a~partial elliptic Dirichlet-to-Neumann map
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 3, pp. 78-94

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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.
Keywords: inverse problem; stability; Schrödinger equation. 
@article{VYURU_2015_8_3_a4,
     author = {M. Choulli and Y. Kian and E. Soccorsi},
     title = {Double logarithmic stability in the identification of a scalar potential by~a~partial elliptic {Dirichlet-to-Neumann} map},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {78--94},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2015_8_3_a4/}
}
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M. Choulli; Y. Kian; E. Soccorsi. Double logarithmic stability in the identification of a scalar potential by~a~partial elliptic Dirichlet-to-Neumann map. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 3, pp. 78-94. http://geodesic.mathdoc.fr/item/VYURU_2015_8_3_a4/