Diffraction of singularities for the wave equation on manifolds with corners

Richard Melrose, András Vasy, Jared Wunsch

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We 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, we show that the singularities which are diffracted by the corners (i.e., loosely speaking, which are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, we 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 our 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.

Original languageEnglish (US)
Pages (from-to)1-142
Number of pages142
JournalAsterisque
Issue number351
StatePublished - Jan 1 2013

ASJC Scopus subject areas

  • Mathematics(all)

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