Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case

2012/08/31 by Oana Ivanovici, Gilles Lebeau, Fabrice Planchon · 1 citation
Mathematics · #math.AP #msc:35L20

paper · pdf · doi:10.4007/annals.2014.180.1.7

published as Ann. of Math. (2) 180 (2014), no. 1, 323-380 · 53 pages, 4 figures, to appear in Annals of Math. Fixed typos, added remarks

arxiv created 2013/04/22 · arxiv updated 2021/08/23

Abstract

We consider a model case for a strictly convex domain of dimension d≥ 2 with smooth boundary and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, 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 type singularities in the wave front set.

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