Global existence for energy critical wave equations in 3-d domains

We study the reklationship between Sogge's $L^p$ spectral estimates for the Laplace operator and Strichartz type estimates for the wave operator. As a consequence of this analysis, we obtain that in 3-d domains, the quintic (critical) defocussing wave equation with Dirichlet boundary conditions is globally well posed in the energy space. This extend previous results of Grillakis and Shatah-Struwe on $R^d$.

(joint with G. Lebeau and F. Planchon)