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# Jacob Shapiro, Australian National University – Analysis & PDE Seminar

## February 6, 2019 @ 4:00 pm - 5:00 pm

**Title: ***Standing wave solution for the nonlinear Schrödinger equation on an asymptotically Euclidean manifold.*

**Abstract: **We construct a Poisson operator for the non-linear Helmholtz equation with prescribed incoming boundary data at infinity. We do this by estimating the resolvent between suitable weighted anisotropic Sobolev spaces. This talk is based on joint work in progress with Jesse Gell-Redman, Andrew Hassell, and Junyong Zhang.