2024年第7期第67讲：蒋永生教授学术报告

广州数学大讲坛第七期

第六十七讲——中南财经政法大学蒋永生教授学术报告

题目: Variational analysis of the planar $L_p$ dual Minkowski problem

时间: 2024年10月16日（星期三）下午15:30——18:00

地点: 腾讯会议（会议 ID：577-257-624）

报告人: 蒋永生 教授

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.

报告人简介:

蒋永生，中南财经政法大学教授，博士生导师，研究工作主要集中在偏微分方程和泛函分析等领域；主持研究4项国家自然科学基金项目和1项湖北省自然科学基金项目。研究成果发表《Mathematische Annalen》, 《Journal of Function Analysis》, 《Calc. Var. Partial Differential Equations》, 《Journal of Differential Equations》等学术期刊上。