Diffraction from conormal singularities

TL;DR

This paper demonstrates that for metrics with conormal singularities of class C^{1,eta}, the reflected wave exhibits greater regularity than the incident wave in Sobolev spaces, aiding in multiple scattering analysis.

Contribution

It introduces a regularity result for reflected waves in metrics with conormal singularities, enhancing the understanding of wave behavior in such geometries.

Findings

Reflected waves are more regular than incident waves in Sobolev sense.

Higher order scattering terms can be effectively isolated due to increased regularity.

Results apply to metrics with conormal singularities of class C^{1,eta}.

Abstract

In this paper we show that for metrics with conormal singularities that correspond to class C^{1,\alpha} with \alpha>0, the reflected wave is more regular than the incident wave in a Sobolev sense. This is helpful in the analysis of the multiple scattering series since higher order terms can be effectively `peeled off'.