Recovering the total singularity of a conormal potential from backscattering data
Annales de l'Institut Fourier, Volume 48 (1998) no. 5, p. 1513-1532

The problem of recovering the singularities of a potential from backscattering data is studied. Let $\Omega$ be a smooth precompact domain in ${ℝ}^{n}$ which is convex (or normally accessible). Suppose ${V}_{i}=v+{w}_{i}$ with $v\in {C}_{c}^{\infty }\left({ℝ}^{n}\right)$ and ${w}_{i}$ conormal to the boundary of $\Omega$ and supported inside $\overline{\Omega }$ then if the backscattering data of ${V}_{1}$ and ${V}_{2}$ are equal up to smoothing, we show that ${w}_{1}-{w}_{2}$ is smooth.

On étudie le problème de la restitution de singularités d’un potentiel de la rétrodiffusion. Soit $\Omega$ un domaine précompact, convexe et ${C}^{\infty }$. Soit ${V}_{i}=v+{w}_{i}$ avec $v\in {C}_{c}^{\infty }\left({ℝ}^{n}\right)$ et ${w}_{i}$ conormale au bord de $\Omega$ et avec support dans $\overline{\Omega }$; si les données de la rétrodiffusion de ${V}_{1}$ et ${V}_{2}$ sont égaux, alors ${V}_{1}-{V}_{2}\in {C}^{\infty }$.

@article{AIF_1998__48_5_1513_0,
author = {Joshi, Mark S.},
title = {Recovering the total singularity of a conormal potential from backscattering data},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {48},
number = {5},
year = {1998},
pages = {1513-1532},
doi = {10.5802/aif.1664},
zbl = {0918.35140},
mrnumber = {2000b:35272},
language = {en},
url = {http://www.numdam.org/item/AIF_1998__48_5_1513_0}
}

Joshi, Mark S. Recovering the total singularity of a conormal potential from backscattering data. Annales de l'Institut Fourier, Volume 48 (1998) no. 5, pp. 1513-1532. doi : 10.5802/aif.1664. http://www.numdam.org/item/AIF_1998__48_5_1513_0/

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