Propagation of singularities for the wave equation on manifolds with corners
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 20, 16 p.

In this talk 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× t , P=D t 2 -Δ M , and uH loc 1 (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, [7]. 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).

These notes are a summary of [17], where the detailed proofs appear.

Classification : 58J47,  35L20
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     title = {Propagation of singularities for the wave equation on manifolds with corners},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
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Vasy, András. Propagation of singularities for the wave equation on manifolds with corners. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2004-2005), Exposé no. 20, 16 p. http://www.numdam.org/item/SEDP_2004-2005____A20_0/

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