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) |
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Pages (from-to) | 235-299 |
Number of pages | 65 |
Journal | Inventiones Mathematicae |
Volume | 156 |
Issue number | 2 |
DOIs | |
State | Published - 2004 |
ASJC Scopus subject areas
- General Mathematics