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

Ramona Anton

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

Analysis of PDEs 2007-05-23 v1

Authors: Ramona Anton

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.

Keywords

nonlinear Schrodinger equation Strichartz inequality Lipschitz metric Dirichlet boundary Cauchy problem wellposedness

Cite

@article{arxiv.math/0512639,
  title  = {Strichartz Inequalities for Lipschitz Metrics on Manifolds and Nonlinear Schrodinger Equation on Domains},
  author = {Ramona Anton},
  journal= {arXiv preprint arXiv:math/0512639},
  year   = {2007}
}

Comments

32 pages

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