# Propagation of singularities for the wave equation on manifolds with corners

András Vasy^{[1]}

- [1] Department of Mathematics, MIT and Northwestern University

Séminaire Équations aux dérivées partielles (2004-2005)

- Volume: 2004-2005, page 1-16

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topVasy, András. "Propagation of singularities for the wave equation on manifolds with corners." Séminaire Équations aux dérivées partielles 2004-2005 (2004-2005): 1-16. <http://eudml.org/doc/11110>.

@article{Vasy2004-2005,

abstract = {In this talk we describe the propagation of $\{\mathcal\{C\}\}^\{\infty \}$ and Sobolev singularities for the wave equation on $\{\mathcal\{C\}\}^\{\infty \}$ manifolds with corners $M$ equipped with a Riemannian metric $g$. That is, for $X=M\times \mathbb\{R\}_t$, $P=D_t^2-\Delta _M$, and $u\in H^1_\{\{\text\{loc\}\}\}(X)$ solving $Pu=0$ with homogeneous Dirichlet or Neumann boundary conditions, we show that $\operatorname\{WF\}_\{\{\text\{b\}\}\}(u)$ is a union of maximally extended generalized broken bicharacteristics. This result is a $\{\mathcal\{C\}\}^\{\infty \}$ 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.},

affiliation = {Department of Mathematics, MIT and Northwestern University},

author = {Vasy, András},

journal = {Séminaire Équations aux dérivées partielles},

language = {fre},

pages = {1-16},

publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Propagation of singularities for the wave equation on manifolds with corners},

url = {http://eudml.org/doc/11110},

volume = {2004-2005},

year = {2004-2005},

}

TY - JOUR

AU - Vasy, András

TI - Propagation of singularities for the wave equation on manifolds with corners

JO - Séminaire Équations aux dérivées partielles

PY - 2004-2005

PB - Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 2004-2005

SP - 1

EP - 16

AB - In this talk we describe the propagation of ${\mathcal{C}}^{\infty }$ and Sobolev singularities for the wave equation on ${\mathcal{C}}^{\infty }$ manifolds with corners $M$ equipped with a Riemannian metric $g$. That is, for $X=M\times \mathbb{R}_t$, $P=D_t^2-\Delta _M$, and $u\in H^1_{{\text{loc}}}(X)$ solving $Pu=0$ with homogeneous Dirichlet or Neumann boundary conditions, we show that $\operatorname{WF}_{{\text{b}}}(u)$ is a union of maximally extended generalized broken bicharacteristics. This result is a ${\mathcal{C}}^{\infty }$ 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.

LA - fre

UR - http://eudml.org/doc/11110

ER -

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