四阶薛定谔方程 Strichtartz 不等式的极值函数
经典分析与常微分方程
2024-10-25 v3 偏微分方程分析
摘要
本文考虑 上四阶薛定谔方程的 Strichartz 不等式。我们利用由端点型分解与稳相法得到的线性轮廓分解，证明极值函数存在。基于极值函数的存在性，我们研究相应的欧拉-拉格朗日方程，证明极值函数具有指数衰减，从而必为解析函数。
引用
@article{arxiv.2210.06695,
title = {Extremizers for the Strichartz Inequality for a Fourth-Order Schr\"odinger Equation},
author = {Boning Di and Ryan Frier},
journal= {arXiv preprint arXiv:2210.06695},
year = {2024}
}
备注
15 pages; The authors would also like to thank Ren\'e Quilodr\'an for pointing out an error in the original version of the paper, as well as providing additional sources for the problem