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Strichartz inequalities for Lipschitz metrics on manifolds and nonlinear Schrödinger equation on domains

Ramona Anton — 2008

Bulletin de la Société Mathématique de France

We prove wellposedness of the Cauchy problem for the nonlinear Schrödinger 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.

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