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Jeffrey Galkowski, Northeastern University – Wunsch/PDE Mini-school
December 6, 2018 @ 4:00 pm - 5:00 pm
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Title: Optimal Resolvent Estimates in Non-trapping Geometries
Abstract: In this talk we discuss how propagation estimates can be used to prove resolvent estimates in non-trapping geometries. We will introduce the notion of defect measures and prove propagation estimates in this setting. We will then use these estimates to prove a non-trapping resolvent estimate and finally refine the estimates to give optimal bounds on the resolvent. Time permitting we discuss the necessary modification when the manifold has a boundary.