Optimal Strichartz estimates for solutions of linear wave equations are well known in the free space.
These estimates have far reaching applications in the study of non linear waves and harmonic analysis.
For linear waves inside a general bounded domain, the first results have been obtained by Smith and Sogge (Acta-Math 2007). In the case of the interior of a strictly convex domain, better estimates have been proved by Ivanovici-Lebeau-Planchon (Annals of Math, 2014).
In this talk, I will present recent results improving all the previous results, obtained in collaboration with Ivanovici, Lascar and Planchon.