arXiv subjects

Ljudevit Palle

Publications and source records attributed to Ljudevit Palle.

2 recordsLinked to original sources

arXiv2020

Strichartz estimates for mixed homogeneous surfaces in three dimensions

We obtain sharp mixed norm Strichartz estimates associated to mixed homogeneous surfaces in $\mathbb{R}^3$. Both cases with and without a damping factor are considered. In the case when a damping factor is considered our results yield a wide generalization of a result of Carbery, Kenig, and Ziesler [CKZ13]. 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 the paper of Ginibre and Velo [GV92], and by using the recently developed methods by Ikromov and Müller [IM16].

math.AP↗

arXiv2019

Mixed norm Strichartz-type estimates for hypersurfaces in three dimensions

In their work [IM16] I.A. Ikromov and D. Müller proved the full range $L^p-L^2$ Fourier restriction estimates for a very general class of hypersurfaces in $\R^3$ which includes the class of real analytic hypersurfaces. In this article we partly extend their results to the mixed norm case where the coordinates are split in two directions, one tangential and the other normal to the surface at a fixed given point. In particular, we resolve completely the adapted case and partly the non-adapted case. In the non-adapted case the case when the linear height $h_\text{lin}(ϕ)$ is below two is settled completely.

math.CA↗