Strichartz estimates for mixed homogeneous surfaces in three dimensions

Palle, Ljudevit

doi:10.2140/apde.2023.16.173

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Strichartz estimates for mixed homogeneous surfaces in three dimensions

Ljudevit Palle

Vol. 16 (2023), No. 1, 173–232

DOI: 10.2140/apde.2023.16.173

Abstract

We obtain sharp mixed-norm Strichartz estimates associated to mixed homogeneous surfaces in $ℝ^{3}$ . Cases with and without a damping factor are both considered. In the case when a damping factor is considered our results yield a wide generalization of a result of Carbery, Kenig, and Ziesler for homogeneous polynomial surfaces in $ℝ^{3}$ . The approach we use is to first classify all possible singularities locally, after which one can tackle the problem by appropriately modifying the methods from a paper of Ginibre and Velo, and by using the recently developed methods by Ikromov and Müller.

Keywords

Strichartz estimates, Fourier restriction, oscillatory integrals, classification of singularities, mixed homogeneous, mixed-norm

Mathematical Subject Classification

Primary: 35B45, 42B15

Milestones

Received: 19 April 2020

Revised: 27 March 2021

Accepted: 19 May 2021

Published: 14 April 2023

Authors

Ljudevit Palle
Christian-Albrechts-Universität zu Kiel Kiel Germany

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Vol. 16, No. 1, 2023