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Propagation of singularities for the wave equation on conic manifolds

Richard Melrose·Jared Wunsch
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Abstract

For the wave equation associated to the Laplacian on a compact manifold with boundary with a conic metric (with respect to which the boundary is metrically a point) the propagation of singularities through the boundary is analyzed. Under appropriate regularity assumptions the diffracted, non-direct, wave produced by the boundary is shown to have Sobolev regularity greater than the incoming wave.

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Richard Melrose, Jared Wunsch. 2001-11-23. Propagation of singularities for the wave equation on conic manifolds. https://arxiv.org/abs/math/0111255

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