The leading singularity of the scattering kernel for a transparent obstacle (Q1086750)

For the wave equation the scattering of waves from a transparent obstacle with boundary Y is considered. Across Y the index of refraction is assumed to be continuous but non-smooth. Then, for directions near backscattering, the leading singularity of the Schwartz kernel of the scattering operator is shown to be given by the supporting function of the obstacle. This singularity is conormal. In addition, it is shown that its order is one step lower when compared with the singularity in the case, studied before by Majda-Taylor and Petkov, where the index of refraction has a jump discontinuity across Y.