Propagation of singularities for the wave equation on manifolds with corners | Annals of Mathematics

Abstract In this paper we describe the propagation of ∞ and Sobolev singularities for the wave equation on ∞ manifolds with corners M equipped with a Riemannian metric g. That is, for X=M×ℝt, P=D2t−ΔM, and u∈H1loc(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 ∞ 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).

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数学年刊(Annals of Mathematics)

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