陈露副研究员学术报告

时间：9月12号下午2:30

地点: 理学院三楼会议室

题目：Title: Existence and Nonexistence of Extremals for the Adams inequalities in R4.

Abstract: Much work has been done with respect to the existence of extremals of the critical Trudinger-Moser inequalities in unbounded domain. However, whether there exist extremal functions for the critical Adams inequalities in unbounded domain still remains open. The classical blow-up procedure can not apply to solving the existence because of the presence of P\'{o}lya-Szeg\"{o}\ type inequality. In this paper, we develop some new ideas based on the sharp Fourier rearrangement principle,sharp constants of the higher-order Gagliardo-Nirenberg inequalities and poly-harmonic truncations to study the existence and nonexistence of the maximizers for the Adams inequalities. Our results also provides a further insight on the existence or nonexistence of extremals for Adams inequality which has not been noticed before, even in the case of Trudinger-Moser inequality.

陈露，北京理工大学副研究员，博士毕业于北京师范大学，研究领域为几何不等式的最佳常数问题及其在非线性偏微分方程中的应用。现从事于几何不等式的最佳常数以及偏微分方程的研究。目前主要研究兴趣为临界的Trudinger-Moser-Adams不等式极值函数的存在性及相关椭圆方程量化性质的研究。

相关研究成果发表在Transactions of the American Mathematical Society, Journal of Functional Analysis ,Calculus of Variations and Partial Differential Equations,Revista matematica iberoamericana,

Potential Analysis等国际知名数学发表期刊论文10余篇。