报告题目1：Quasilinear mixed problems with different orders

报告人：张超教授，哈尔滨工业大学

报告时间：2024年10月17日（周四）8:30-9:30

会议地点：腾讯会议：943-401-638

摘要：In recent years, the mixed local and nonlocal problems have been widely studied owing to its essential applications in plasma physics and biology. In this talk, we consider the quasilinear mixed problems with different orders. By using the De Giorgi type iteration and expansion of positivity, we study the local behaviour of the minimizers of such problems, involving the local boundedness, the local Holder continuity, and Harnack type inequality.

报告人简介：张超，哈尔滨工业大学，教授，本科和硕士毕业于吉林大学，博士毕业于北京大学。主要从事函数空间理论、非线性椭圆和抛物型偏微分方程的适定性和正则性等方面的研究，在Math. Ann., J. London Math. Soc, J. Func. Anal., Calc. Var. Partial Differential Equations, Indiana Univ. Math. J., Israel J. Math., Int. Math. Res. Not. IMRN, J. Differential Equations, J. Geom. Anal.和Bull. Lond. Math. Soc.等权威期刊发表论文50余篇。目前担任黑龙江省数学会秘书长，国际SCI期刊《Advances in Nonlinear Analysis》编委。

报告题目2：Higher order semilinear problems on hyperbolic spaces

报告人：李俊钢教授，中国科学技术大学

报告时间：2024年10月17日（周四）9:30-10:30

会议地点：腾讯会议：943-401-638

摘要：In this talk we will discuss some recent progress on semilinear equations involving GJMS operators on hyperbolic spaces. Due to the geometric structure of the ambient space, classical calculus of variation method needs to be modified and new techniques regarding functional inequalities, Green's function estimates, moving plane methods and blow-up analysis will be introduced.

报告人简介：李俊钢，中国科学技术大学，教授，主要研究方向为几何不等式，如双曲空间，乘积流形上的Trudinger-Moser不等式，Adams不等式等。相关工作发表在Adv. Math, T. Am. Math. Soc., Calc.Var. Partial. Differential Equations等国际著名SCI学术期刊。

报告题目3：Recent progress on optimal stability of geometric inequality with dimension-dependent or order-dependent constans

报告人：陈露副教授，北京理工大学

报告时间：2024年10月17日（周四）10:30-11:30

会议地点：腾讯会议：943-401-638

摘要：In this talk, we will first introuduce the sharp geometric inequality and their stability. Then we present recent progress on the optimal stability for Hardy- Littlewood-Sobolev (HLS) inequality, fractional Sobolev inequality, Log-Sobolev inequality and trace Sobolev inequality. Some interesting open problems will be also discussed.

报告人简介：陈露，北京理工大学长聘副教授，博导。2018年博士毕业于北京师范大学，在Moser-Truding-Adams不等式的最佳常数和极值问题、几何不等式的量化稳定性、指数临界增长的薛定谔方程基态解、双曲空间上波方程的散射理论等方面取得了重要的进展，相关结果发表在Proc.Lond.Math.Soc., Adv.Math., Trans.AMS., J.Funct.Anal., Rev.Mat.Iberoam., Calc.Var.&PDE.等国际学术期刊。

报告题目4：Anisotropic weighted isoperimetric inequality and its applications

报告人：朱茂春教授，南京理工大学

报告时间：2024年10月17日（周四）14:30-15:30

会议地点：腾讯会议：943-401-638

摘要：In this talk, I will report our recent work on the anisotropic weighted isoperimetric inequality. Based on this isoperimetric inequality, we can obtain a classification result for the singular Liouville equation involving the Finsler N-Laplacian. Finally, by the classification result and weighted isoperimetric inequality, we show the existence of extremals for the anisotropic singular Trudinger-Moser inequalities on any bounded domains through the classic blow-up analysis.

报告人简介：朱茂春，南京理工大学，教授，2013年博士毕业于西北工业大学理学院，曾赴意大利米兰理工大学联合培养。主要研究方向为几何不等式、非线性微分方程等。相关研究工作发表在Adv. Math.、Analysis & PDE.、Calc. Var. & PDE.、J. Differntial Equations.、Proc. Amer. Math. Soc.等国际知名SCI学术期刊。

报告题目5：Classification of critical Schrodinger system with p-Laplacian

报告人：刘招教授，江西科技师范大学

报告时间：2024年10月17日（周四）15:30-16:30

会议地点：腾讯会议：943-401-638

摘要：In this talk, we discuss critical Schrodinger system with p-Laplacian, we establish regularity and the sharp estimates on asymptotic behaviors for any positive solution. Then, we prove that all positive solutions are radially symmetric and strictly decreasing about some point. Moreover, we obtain the uniqueness and complete classification of positive solution.

报告人简介：刘招，江西科技师范大学数学科学学院教授，江西省青年井冈学者。主要从事偏微分方程、最优几何不等式等领域研究。在Math Ann, Transactions of AMS, SIAM JMA, Calc. Var. PDE, J. Differential Equations等期刊上发表SCI论文26篇，主持国家自然科学基金项目3项，省部级项目5项。

邀请人：非线性分析与PDE团队