Abstract
We consider the Schrodinger equation on a half space in any dimension with a class of nonhomogeneous boundary conditions including Dirichlet, Neuman and the so-called transparent boundary conditions. Building upon recent local in time Strichartz estimates (for Dirichlet boundary conditions), we obtain global Strichartz estimates for initial data in H s , 0 ¤ s ¤ 2 and boundary data in a natural space H s. For s ¥ 1{2, the issue of compatibility conditions requires a thorough analysis of the H s space. As an application we solve nonlinear Schrodinger equations and construct global asymptotically linear solutions for small data. A discussion is included on the appropriate notion of scattering in this framework, and the optimality of the H s space.
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