Sharp Strichartz estimates for some variable coefficient Schr\"{o}dinger operators on $\mathbb{R}\times\mathbb{T}^2$

Serena Federico; Gigliola Staffilani

doi:10.3934/mine.2022033

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arXiv · 2106.11940

Sharp Strichartz estimates for some variable coefficient Schr\"{o}dinger operators on $\mathbb{R}\times\mathbb{T}^2$

Serena Federico·Gigliola Staffilani

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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.

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Serena Federico, Gigliola Staffilani. 2021-06-22. Sharp Strichartz estimates for some variable coefficient Schr\"{o}dinger operators on $\mathbb{R}\times\mathbb{T}^2$. https://doi.org/10.3934/mine.2022033

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