  We prove that the quintic Schrodinger equation with Dirichlet boundary
conditions is locally well posed for H^{1}_{0} data on any smooth, non-trapping
domain of R^3. The key ingredient is a smoothing effect in L^{5}_{x}L^{2}_{t}
for the linear equation. We also derive scattering results for the whole range
of defocusing sub-quintic Schrodinger equations outside star-shaped domains.
