Diffractive Theorems for the Wave Equation with Inverse Square Potential

Details Diffractive Theorems for the Wave Equation with Inverse Square Potential Diffractive Theorems for the Wave Equation with Inverse Square Potential

2009-10-19

arxiv.org/abs/0910.3696v1

Mathematics

Analysis of PDEs

41 pages, 6 figures

Scientific paper

We first establish the presence of a diffractive front in the fundamental solution of the wave operator with a diract delta intial condition in two dimensional euclidean space caused by the potentials perturbation on the spherical laplacian. This motivates a result which restricts the propagation of singularities for the wave operator with a more general potential to precisely these diffractive fronts higher dimensional euclidean spaces. This is proven using microlocal energy estimates.

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