Propagation of singularities for the wave equation on manifolds with corners

• 成果类型: Article
• 署名作者: Vasy, Andras
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.168.749
• 发表日期: 2008
• 页码: 749-812
• 关键词: boundary-value-problems; many-body scattering

摘要

In this paper we describe the propagation of C-infinity and Sobolev singularities for the wave equation on C-infinity manifolds with corners M equipped with a Riemannian metric g. That is, for X = M x R-t, P = D-t(2) - Delta(M), and u is an element of H-loc(1) (X) solving Pu = 0 with homogeneous Dirichlet or Neumann boundary conditions, we show that WFb(u) is a union of maximally extended generalized broken bicharacteristics. This result is a C-infinity counterpart of Lebeau's results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary, [11]. Our methods rely on b-microlocal positive commutator estimates, thus providing a new proof for the propagation of singularities at hyperbolic points even if M has a smooth boundary (and no corners).