  We prove localized energy estimates for the wave equation in domains with a
strictly concave boundary when homogeneous Dirichlet or Neumann conditions are
imposed. By restricting the solution to small, frequency dependent, space time
collars of the boundary, it is seen that a stronger gain in regularity can be
obtained relative to the usual energy estimates. Mixed norm estimates of
Strichartz and square function type follow as a result, using the energy
estimates to control error terms which arise in a wave packet parametrix
construction. While the latter estimates are not new for Dirichlet conditions,
the present approach provides an avenue for treating these estimates when
Neumann conditions are imposed. The method also treats Schr\"odinger equations
with time independent coefficients.
