Propagation of singularities for the wave equation on conic manifolds

Richard Melrose; Jared Wunsch

doi:10.1007/s00222-003-0339-y

Propagation of singularities for the wave equation on conic manifolds

Richard Melrose^*, Jared Wunsch

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

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.

Original language	English (US)
Pages (from-to)	235-299
Number of pages	65
Journal	Inventiones Mathematicae
Volume	156
Issue number	2
DOIs	https://doi.org/10.1007/s00222-003-0339-y
State	Published - 2004

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Mathematics(all)

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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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AU - Wunsch, Jared

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AB - 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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Propagation of singularities for the wave equation on conic manifolds

Abstract

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