On the supercritical defocusing NLW outside a ball

We study a defocusing semilinear wave equation, with a power nonlinearity | u| p-1u, defined outside the unit ball of Rn, n≥ 3 , with Dirichlet boundary conditions. We prove that if p> n+ 3 and the initial data are nonradial perturbations of large radial data, there exists a global smooth solution. The solution is unique among energy class solutions satisfying an energy inequality. The main tools used are the Penrose transform and a Strichartz estimate for the exterior linear wave equation perturbed with a large, time dependent potential.