Time decay of Lp norms for solutions of the wave equation on exterior domains

摘要: We consider global estimates for the time dependence of spatial L p norms solutions to wave equation on exterior a smooth compact strictly convex obstacle in ℝn, n ≥ 2, with vanishing Dirichlet data boundary: $$ \square u = 0\,{\text{on}}\,\Omega \times \mathbb{R},\,u\left( 0 \right) f_0 ,u_t \left( f_1 ,u\left| {_{\partial \Omega \mathbb{R}} 0} \right. $$ (1.1) .