偏微分方程研讨班：The extremizer problem for the Tomas-Stein inequality for the two dimensional sphere

发布时间：2024-06-06 【字体：大中小】

中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

偏微分方程研讨班

报告人：邵双林副教授（堪萨斯大学）

题目：The extremizer problem for the Tomas-Stein inequality for the two dimensional sphere.

时间：2024.06.13（星期四）10:00-11:00

地点：思源楼S615

摘要：Motivated by the recent progress of the concentration-compactness approach in solving the energy-critical and mass-critical dispersive equations such as nonlinear Schr\”odinger equations and the nonlinear wave equations, we investigated the extremizer problem for the Tomas-Stein inequality for the two dimensional sphere. We prove that extremizers exist and they are also smooth. We also prove that constant functions are local extremizers. The method is the concentration-compactness facilitated by a refined Bourgain-type Tomas-Stein inequality. This is a joint work with Michael Christ.

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