Strichartz Inequalities for Lipschitz Metrics on Manifolds and Nonlinear Schrodinger Equation on Domains

摘要

We prove wellposedness of the Cauchy problem for the nonlinear Schrodingerequation for any defocusing power nonlinearity on a domain of the plane withDirichlet boundary conditions. The main argument is based on a generalizedStrichartz inequality on manifolds with Lipschitz metric.