报告题目：Variational analysis of the planar $L_p$ dual Minkowski problem for $q\geq2$

报告人：蒋永生教授，中南财经政法大学

报告时间：2023年04月13日09:00—10:00

报告地点：20-306

报告摘要：In this talk, we consider the planar $L_p$ dual Minkowski problem. By studying the nonlinear problems characterizing the planar $L_p$ dual Minkowski problem in Sobolev spaces, several sharp functional inequalities associated with the $L_p$ dual curvature measures are established to generalize the classical inequalities, such as the Wirtinger's inequality and the Blaschke-Santal\'{o} inequality. Based on these new sharp functional inequalities, various existence results for the planar $L_p$ dual Minkowski problem are obtained for integrable data. Compared with the uniqueness results, the non-uniqueness and multiple $\pi-$periodic solutions are also obtained for $p=0$ through variational analysis. This talk is based on the joint works with Prof. Yong Huang, Prof. Zhengping Wang and Prof. Yonghong Wu.

报告人简介： 蒋永生，中南财经政法大学教授。主要研究方向为偏微分方程和非线性泛函分析等。研究结果发表在Math. Ann., J. Funct. Anal., Calc. Var. PDE, J. Differential Equations, Commun. Contemp. Math.等学术期刊上。

邀请人：非线性分析与PDE团队