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arxiv: 1709.03836 · v1 · pith:IWNCOHAInew · submitted 2017-09-12 · 🧮 math.AP

Strichartz estimates without loss outside two strictly convex obstacles

David Lafontaine This is my paper
classification 🧮 math.AP
keywords lossconvexestimatesobstaclesoutsidestrichartzstrictlywithout
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We prove global Strichartz estimates without loss outside two strictly convex obstacles, combining arguments from M.Ikawa (1982,1988) with more recent ones inspired by N.Burq, C.Guillarmou, and A. Hassell (2010) and O. Ivanovici (2010). This is to be contrasted with the loss in the smoothing estimate for the Schr\"odinger equation with Dirichlet boundary conditions in the presence of a trapped geodesic.

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  1. On scattering and profile decomposition for critical nonlinear waves outside weakly trapping obstacles

    math.AP 2026-04 unverdicted novelty 8.0

    Scattering is shown for critical defocusing waves outside weakly trapping obstacles via infinite-time linear and nonlinear profile decompositions, assuming global Strichartz estimates, weak non-trapping, no reconcentr...