paper

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

arXiv:math/0512639

Abstract

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.

32 pages

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