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The Fundamental Solution and Strichartz Estimates for the Schrödinger Equation on Flat Euclidean Cones

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Abstract

We study the Schrödinger equation on a flat euclidean cone \({\mathbb{R}_+ \times \mathbb{S}^1_\rho}\) of cross-sectional radius ρ > 0, developing asymptotics for the fundamental solution both in the regime near the cone point and at radial infinity. These asymptotic expansions remain uniform while approaching the intersection of the “geometric front,” the part of the solution coming from formal application of the method of images, and the “diffractive front” emerging from the cone tip. As an application, we prove Strichartz estimates for the Schrödinger propagator on this class of cones.

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  1. Department of Mathematics, Northwestern University, 2033 Sheriden Road, Evanston, IL, 60208, USA

    G. Austin Ford

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  1. G. Austin Ford
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Correspondence to G. Austin Ford.

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Communicated by S. Zelditch

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Austin Ford, G. The Fundamental Solution and Strichartz Estimates for the Schrödinger Equation on Flat Euclidean Cones. Commun. Math. Phys. 299, 447–467 (2010). https://doi.org/10.1007/s00220-010-1050-7

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