Abstract
In this paper we describe the propagation of C°° and Sobolev singularities for the wave equation on C°° manifolds with corners M equipped with a Riemannian metric g. That is, for X = M x R t , P = D 2 t - Δ M , and u ∈ H 1 loc (X) solving Pu = 0 with homogeneous Dirichlet or Neumann boundary conditions, we show that WF b (u) is a union of maximally extended generalized broken bicharacteristics. This result is a C°° 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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