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 Ω be a smooth precompact domain in n which is convex (or normally accessible). Suppose V i =v+w i with vC c ( n ) and w i conormal to the boundary of Ω and supported inside 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.

On étudie le problème de la restitution de singularités d’un potentiel de la rétrodiffusion. Soit Ω un domaine précompact, convexe et C . Soit V i =v+w i avec vC c ( n ) et w i conormale au bord de Ω et avec support dans Ω ¯; si les données de la rétrodiffusion de V 1 et V 2 sont égaux, alors V 1 -V 2 C .

@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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