Strichartz estimates for the wave equation on manifolds with boundary

Abstract

We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain global existence in the subcricital case, as well as global existence for the critical equation with small data. We also can use our Strichartz estimates to prove scattering results for the critical wave equation with Dirichlet boundary conditions in 3-dimensions.