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SUMMARY:Dispersive estimates for the wave equation in strictly convex doma
 ins - Oana Ivanovici (CNRS and Université de Nice Sophia-Antipolis)
DTSTART:20140224T150000Z
DTEND:20140224T160000Z
UID:TALK50281@talks.cam.ac.uk
CONTACT:25129
DESCRIPTION:In recent years\, following results on dispersive estimates\nf
 or low regularity metrics\, substantial progress has been made on\ndispers
 ive estimates for the wave and Schrodinger equations on\ndomains. Here we 
 report on recent work to obtain a sharp dispersion\nestimate. For this\, w
 e rely on a precise description of the wave front\n(or the pseudo-spheres\
 , e.g. surfaces reached by light emanating from\na point after a fixed amo
 unt of time) and on a suitable microlocal\nparametrix construction near th
 e boundary\, for the wave equation\ninside strictly convex domains\, subje
 ct to Dirichlet boundary\ncondition. Such a parametrix allows to follow wa
 ve packets propagating\nalong the boundary with a large number of reflecti
 ons. In the process\nwe encounter Fourier Integral Operators whose canonic
 al forms\ncorrespond to cusp and swallowtail singularities\, and which acc
 ount\nfor the loss (compared to the boundary less case) in dispersive\nest
 imates. This is joint work with Gilles Lebeau and Fabrice Planchon.
LOCATION:CMS\, MR13
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