Recovering the total singularity of a conormal potential from backscattering data

Joshi, Mark S.

Joshi, Mark S.

Annales de l'Institut Fourier, Tome 48 (1998), p. 1513-1532 / Harvested from Numdam

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Résumé
Abstract

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

The problem of recovering the singularities of a potential from backscattering data is studied. Let $Ω$ be a smooth precompact domain in $ℝ^{n}$ which is convex (or normally accessible). Suppose $V_{i} = v + w_{i}$ with $v \in C_{c}^{\infty} (ℝ^{n})$ and $w_{i}$ conormal to the boundary of $Ω$ and supported inside $\bar{Ω}$ 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.

Publié le : 1998-01-01

MR 2000b:35272 | Zbl 0918.35140

DOI : https://doi.org/10.5802/aif.1664

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     author = {Joshi, Mark S.},
     title = {Recovering the total singularity of a conormal potential from backscattering data},
     journal = {Annales de l'Institut Fourier},
     volume = {48},
     year = {1998},
     pages = {1513-1532},
     doi = {10.5802/aif.1664},
     mrnumber = {2000b:35272},
     zbl = {0918.35140},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 48 (1998) pp. 1513-1532. doi : 10.5802/aif.1664. http://gdmltest.u-ga.fr/item/AIF_1998__48_5_1513_0/

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