STRICHARTZ ESTIMATES FOR THE WAVE EQUATION INSIDE CYLINDRICAL CONVEX DOMAINS

We establish local-in-time Strichartz estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains Omega subset of R-3 with smooth boundary partial derivative Omega not equal empty set. The key ingredients to prove Strichartz estimates are dispersive estimates, energy estimates, interpolation and TT* arguments. Strichartz estimates for waves inside an arbitrary domain Omega have been proved by Blair, Smith and Sogge ['Strichartz estimates for the wave equation on manifolds with boundary', Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009), 1817-1829]. We provide a detailed proof of the usual Strichartz estimates from dispersive estimates inside cylindrical convex domains for a certain range of the wave admissibility.