Sharp Strichartz estimates for some variable coefficient Schr\"{o}dinger operators on $\mathbb{R}\times\mathbb{T}^2$
Analysis of PDEs
2022-01-14 v2
Abstract
In the first part of the paper we continue the study of solutions to Schr\"odinger equations with a time singularity in the dispersive relation and in the periodic setting. In the second we show that if the Schr\"odinger operator involves a Laplace operator with variable coefficients with a particular dependence on the space variables, then one can prove Strichartz estimates at the same regularity as that needed for constant coefficients. Our work presents a two dimensional analysis, but we expect that with the obvious adjustments similar results are available in higher dimensions.
Cite
@article{arxiv.2106.11940,
title = {Sharp Strichartz estimates for some variable coefficient Schr\"{o}dinger operators on $\mathbb{R}\times\mathbb{T}^2$},
author = {Serena Federico and Gigliola Staffilani},
journal= {arXiv preprint arXiv:2106.11940},
year = {2022}
}