Sharp Strichartz estimates in spherical coordinates

Robert Schippa

doi:10.3934/cpaa.2017100

Article Contents

2017, Volume 16, Issue 6: 2047-2051. Doi: 10.3934/cpaa.2017100

This issue Previous Article Two-and multi-phase quadrature surfaces Next Article Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition

Sharp Strichartz estimates in spherical coordinates

Robert Schippa^,

Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31,33501 Bielefeld, Germany

* Corresponding author
* Corresponding author

Received: November 2016

Revised: May 2017

Published: September 2017

Financial support by the German Science Foundation (IRTG 2235) is gratefully acknowledged

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Abstract

We prove Strichartz estimates found after adding regularity in the spherical coordinates for Schrödinger-like equations. The obtained estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages, which were obtained in [5]. We discuss sharpness making use of a modified Knapp-type example.

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Mathematics Subject Classification: Primary: 42B37; Secondary: 35Q40.

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References

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