Abstract
In this note we consider a strictly convex domain Ω⊂ℝ d of dimension d≥2 with smooth boundary ∂Ω≠∅ and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the dispersive estimates.
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