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Diffraction of Singularities for the Wave Equation on Manifolds with Corners
Richard Melrose, Massachusetts Institute of Technology, Cambridge, MA, András Vasy, Stanford University, CA, and Jared Wunsch, Northwestern University, Evanston, IL
A publication of the Société Mathématique de France.
cover
Astérisque
2013; 136 pp; softcover
Number: 351
ISBN-13: 978-2-85629-367-6
List Price: US$52
Member Price: US$41.60
Order Code: AST/351
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The authors consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, the authors show that the singularities which are diffracted by the corners (i.e., loosely speaking, are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, the authors show that subject to a hypothesis of nonfocusing, diffracted wavefronts of any solution to the wave equation are smoother than the incident singularities. These results extend the authors' previous work on edge manifolds to a situation where the fibers of the boundary fibration, obtained here by blowup of the corner in question, are themselves manifolds with corners.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in wave equations, wavefront sets, and diffraction.

Table of Contents

  • Introduction
  • Geometry: metric and Laplacian
  • Bundles and bicharacteristics
  • Edge-b calculus
  • Differential-pseudodifferential operators
  • Coisotropic regularity and non-focusing
  • Edge propagation
  • Propagation of fiber-global coisotropic regularity
  • Geometric theorem
  • Index of notation
  • Bibliography
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