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Abstract
The purpose of this thesis is to investigate the diffraction of singularities of solutions to the linear elastic equation on manifolds with edge singularities. Such manifolds are modeled on the product of a smooth manifold and a cone over a compact fiber. For the fundamental solution, the initial pole generates a pressure wave (p-wave), and a secondary, slower shear wave (s-wave). If the initial pole is appropriately situated near the edge, we show that when a p-wave strikes the edge, the diffracted p-waves and s-waves (i.e. loosely speaking, are not limits of p-rays which just miss the edge) generated from such an interaction are weaker in a Sobolev sense than the incident p-wave. More generally, we show that subject to a "coinvolutivity" hypothesis, if a p-singularity (or s-singularity) of any solution strikes the edge, the diffracted p and s wavefronts are smoother that the incident singularity.
