Strichartz estimates and well-posedness for a Schrödinger equation in a half-space with a nonlinear Neumann condition on the boundary

I present some best possible Strichartz estimates and well-posedness results for a Schrödinger equation in a half-space with a nonlinear Neumann condition at the boundary. This problem arises as the natural ``extension" of a nonlocal Schrödinger equation with memory. A key feature of the analysis is the distinction between two regimes of the problem which exhibit different dispersive behaviors and require different functional frameworks. The talk discusses some recent joint work with G. Staffilani and will be non-technical and accessible to graduate students with an interest in analysis and partial differential equations.