Propagation of singularities for the wave equation on conic manifolds

• 成果类型: Article
• 署名作者: Melrose, R; Wunsch, J
• 署名单位: Northwestern University; Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0339-y
• 发表日期: 2004
• 页码: 235-299
• 关键词: fourier integral operators; diffraction

摘要

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.