On extremizers for Strichartz estimates for higher order Schrödinger equations
On extremizers for Strichartz estimates for higher order Schrödinger equations
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高阶薛定谔方程的 Strichartz 估计的极值化
DOI：
10.1090/tran/7223
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发表时间：
2016
影响因子：
1.3
通讯作者：
Ren'e Quilodr'an
中科院分区：
文献类型：
--
作者：
D. O. Silva;Ren'e Quilodr'an
对于适当的一类凸函数$\phi$，我们研究曲面$\{（y，|y| ^2+\phi（y））：y\in\mathbb{R}^2\}$配备投影度量。对于相应的扩张不等式，我们计算了最优常数，并证明了不存在极值解。主要的工具是一个新的比较原则，在所有维度的某些奇异措施的卷积。利用集中紧性的工具，我们进一步研究了一般极值序列的性质。我们的工作直接关系到某些高阶Schr\“odinger方程的Schr\“odinger估计的极值子和最佳常数的研究。特别地，我们解决了最近文献中关于一类四阶Schr“odinger方程极值解存在性的二分法，并在只知道下界的情况下精确地计算了相应的算子范数.
For an appropriate class of convex functions $\phi$, we study the Fourier extension operator on the surface $\{(y, |y|^2+\phi(y)):y\in\mathbb{R}^2\}$ equipped with projection measure. For the corresponding extension inequality, we compute optimal constants and prove that extremizers do not exist. The main tool is a new comparison principle for convolutions of certain singular measures that holds in all dimensions. Using tools of concentration-compactness flavor, we further investigate the behavior of general extremizing sequences. Our work is directly related to the study of extremizers and optimal constants for Strichartz estimates of certain higher order Schr\"odinger equations. In particular, we resolve a dichotomy from the recent literature concerning the existence of extremizers for a family of fourth order Schr\"odinger equations, and compute the corresponding operator norms exactly where only lower bounds were previously known.
Strichartz 范数的热流单调性
影响因子：
2.2
作者：
Bennett J
通讯作者：
Bennett J