Propagation of singularities for the wave equation on conic manifolds

2001/11/23 by Richard Melrose, Melrose, Richard, Jared Wunsch +1 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #35L05 #58J47 (Primary) 58J40 (Secondary) #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #advanced mathematical theories #math-ph #math.AP #math.CA #math.MP #msc:35L05 #msc:58J40 #msc:58J47

paper · pdf · doi:10.48550/arxiv.math/0111255

arxiv created 2001/11/23 · openalex publication_date 2001/11/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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