Stability of the inverse problem in potential scattering at fixed energy

Stefanov, Plamen

Annales de l'Institut Fourier, Tome 40 (1990), p. 867-884 / Harvested from Numdam

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Abstract

Nous prouvons une estimation du type $∥ q_{1} - q_{2} ∥_{L^{\infty}} \leq C φ (∥ A_{q_{1}} - A_{q_{2}} ∥_{R, 3 / 2 - 1 / 2})$ , où $A_{q_{i}} (ω, θ)$ , $i = 1, 2$ est l’amplitude de “scattering” relative au potentiel à support compact $q_{i} (x)$ à un niveau d’énergie fixée $k =$ const., où $φ (t) = (- ln t)^{- δ}$ , $0 < δ < 1$ et $∥ \cdot ∥_{R, 3 / 2 - 1 / 2}$ est une norme définie.

We prove an estimate of the kind $∥ q_{1} - q_{2} ∥_{L^{\infty}} \leq C φ (∥ A_{q_{1}} - A_{q_{2}} ∥_{R, 3 / 2 - 1 / 2})$ , where $A_{q_{i}} (ω, θ)$ , $i = 1, 2$ is the scattering amplitude related to the compactly supported potential $q_{i} (x)$ at a fixed energy level $k =$ const., $φ (t) = (- ln t)^{- δ}$ , $0 < δ < 1$ and $∥ \cdot ∥_{R, 3 / 2 - 1 / 2}$ is a suitably defined norm.

Publié le : 1990-01-01

MR 92d:35217 | Zbl 0715.35082

DOI : https://doi.org/10.5802/aif.1239

@article{AIF_1990__40_4_867_0,
     author = {Stefanov, Plamen},
     title = {Stability of the inverse problem in potential scattering at fixed energy},
     journal = {Annales de l'Institut Fourier},
     volume = {40},
     year = {1990},
     pages = {867-884},
     doi = {10.5802/aif.1239},
     mrnumber = {92d:35217},
     zbl = {0715.35082},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1990__40_4_867_0}
}

Stefanov, Plamen. Stability of the inverse problem in potential scattering at fixed energy. Annales de l'Institut Fourier, Tome 40 (1990) pp. 867-884. doi : 10.5802/aif.1239. http://gdmltest.u-ga.fr/item/AIF_1990__40_4_867_0/

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