Dispersion for the Wave Equation Inside Strictly Convex Domains II: The General Case

We consider the wave equation on a strictly convex domain of dimension at least two with smooth non empty boundary and Dirichlet conditions. construct sharp local in time parametrix then proceed to obtain dispersion estimates: our fixed decay rate for Green function exhibits $t^{1/4}$ loss respect less case. Moreover, we precisely describe where when these losses occur relate them swallowtail type singularities front set, proving that resulting is optimal. derive better than expected Strichartz estimates, balancing lossy long estimates given incidence short ones no loss: three dimensions, it heuristically means that, average only $t^{1/6}$.