Stability of the inverse problem in potential scattering at fixed energy

Stefanov, Plamen

Annales de l'Institut Fourier, Tome 40 (1990) no. 4, pp. 867-884.

Nous prouvons une estimation du type $\parallel q_1-q_2{\parallel }_{L^{\infty }}\le C\phi (\parallel A_{q_1}-A_{q_2}{\parallel }_{R,3/2-1/2})$, où $A_{q_i}(\omega ,\theta )$, $i=1,2$ est l’amplitude de “scattering” relative au potentiel à support compact $q_i\left(x\right)$ à un niveau d’énergie fixée $k=$ const., où $\phi \left(t\right)=(-lnt{)}^{-\delta }$, $0<\delta <1$ et $\parallel ·{\parallel }_{R,3/2-1/2}$ est une norme définie.

We prove an estimate of the kind $\parallel q_1-q_2{\parallel }_{L^{\infty }}\le C\phi (\parallel A_{q_1}-A_{q_2}{\parallel }_{R,3/2-1/2})$, where $A_{q_i}(\omega ,\theta )$, $i=1,2$ is the scattering amplitude related to the compactly supported potential $q_i\left(x\right)$ at a fixed energy level $k=$ const., $\phi \left(t\right)=(-lnt{)}^{-\delta }$, $0<\delta <1$ and $\parallel ·{\parallel }_{R,3/2-1/2}$ is a suitably defined norm.

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