報告題目：Variational analysis of the planar $L_p$ dual Minkows-ki problem

報告時間：2023年4月6日（周四）15:00

報告地點：景中師范中心

報告人：蔣永生

報告人單位：中南財經(jīng)政法大學(xué)

報告簡介：

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. 

報告人簡介：

蔣永生，中南財經(jīng)政法大學(xué)教授，博士生導(dǎo)師。主要研究方向為偏微分方程，非線性泛函分析及其應(yīng)用等。研究結(jié)果發(fā)表在Math. Ann., J. Funct. Anal., Calc. Var. PDE, J. Differential Equations, Sci. China Math.等學(xué)術(shù)期刊上。 

邀請單位：數(shù)學(xué)與統(tǒng)計學(xué)院