报告题目：Sharp functional inequalities associated with the Lp dual curvature measures.

报告人：蒋永生

报告摘要：

The Lp dual curvature measures were recently introduced by Lutwak et al. (Adv Math 329:85-132, 2018) to unify the classical theory of mixed volumes and the newer theory of dual mixed volumes of convex bodies. However, the associated Lp dual Minkowski problems for many important special cases remain open problems. In this talk, we will give several sharp functional inequalities associated with the Lp dual curvature measures, which generalized the classical inequalities, such as the Wirtinger’s inequality and the Blaschke-Santalo inequality. Based on these new sharp ´functional inequalities, various existence results for the planar Lp dual Minkowski problem are obtained for integrable data and general q ≥ 2. Compared with the uniqueness results of π−periodic solutions for p = 0 and q = 2 (in Dohmen and Giga, Proc Japan Acad Ser A Math Sci, 1994; Andrews, J Amer Math Soc, 2003), the non-uniqueness and multiple π−periodic solutions are also obtained for p = 0 and all q > 4.

报告时间: 12月4日（周日）下午15:00—16:00

报告地点：腾讯会议 ID  584 738 185

报告人简介：

蒋永生，中南财经政法大学教授。研究方向为偏微分方程和非线性泛函分析及其应用。先后获得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的资助。研究成果发表在Journal of Function Analysis, Calculus of Variations and Partial Differential Equations，Journal of Differential Equations, Commun.Contemp. Math.,中国科学，数学物理学报等学术期刊上。