In the first part of the paper we continue the study of solutions to Schrödinger equations with a time singularity in the dispersive relation and in the periodic setting. In the second we show that if the Schrödinger 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.

Federico S., Staffilani G. (2022). Sharp Strichartz estimates for some variable coefficient Schrödinger operators on R × T2. MATHEMATICS IN ENGINEERING, 4(4), 1-23 [10.3934/mine.2022033].

Sharp Strichartz estimates for some variable coefficient Schrödinger operators on R × T2

Federico S.;
2022

Abstract

In the first part of the paper we continue the study of solutions to Schrödinger equations with a time singularity in the dispersive relation and in the periodic setting. In the second we show that if the Schrödinger 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.
2022
Federico S., Staffilani G. (2022). Sharp Strichartz estimates for some variable coefficient Schrödinger operators on R × T2. MATHEMATICS IN ENGINEERING, 4(4), 1-23 [10.3934/mine.2022033].
Federico S.; Staffilani G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/844010
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