Dispersive and Strichartz estimates for the wave equation in domains with boundary

Ivanovici, Oana

Journées équations aux dérivées partielles (2010), article no. 11, 19 p.

In this note we consider a strictly convex domain $\Omega \subset {ℝ}^d$ of dimension $d\ge 2$ with smooth boundary $\partial \Omega \ne \varnothing$ 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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