On the energy critical Schrodinger equation in 3D non-trapping domains

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