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

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 .

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.

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

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