The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science
                 Mathematical Analysis and Applications Seminar
                     Lecture Hall, Room 1, Ziskind Building
                       ((((on Tuesday, April 23, 2013))))
                              ((((11:00 - noon))))
                                 Richard Lascar
               Universit\'e Pierre and Marie Curie, Paris, France
                                 will speak on
                        Dispersion for the Wave Equation
                         Inside Strictly Convex Domains

We consider a strictly convex domain with non empty smooth boundary and of
dimension greater than one. We describe dispersion estimates for the wave
equation with Dirichlet boundary conditions. We obtain the optimal fixed time
decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs with
respect to the boundary less case, due to repeated occurrences of swallowtail
types singularities in the wave front set. The study of the model case, i.e.
the Friedlander model, has been achieved in August 2012 by O. Ivanovici, G.
Lebeau and F. Planchon. In this lecture we shall try to discuss the general
case for strictly convex domains, reading carefully the famous result of
Melrose about equivalence of glancing hypersurfaces, and the results of Taylor-
Melrose- Eskin about microlocal parametrices. The main tools are the geometric
constructions of G. Lebeau allowing suitable solutions of the iconal
equations.  A consequence is the so-called Strichartz estimates for the wave
equation inside strictly convex domains with smooth boundaries. The main
application is the existence of global solutions for non linear critical wave
equations though the dispersion presents its own interest.
Joint work with O. Ivanovici, G. Lebeau, F. Planchon.
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Yaeli Malka   <>