Strichartz Inequalities for Lipschitz Metrics on Manifolds and Nonlinear   Schrodinger Equation on Domains
  We prove wellposedness of the Cauchy problem for the nonlinear Schrodinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on manifolds with Lipschitz metric. 
Ramona Anton