报 告 人：李亦

工作单位：纽约城市大学约翰杰分校

报告时间：5月22日9：00

报告网址：Zoom会议 ID：950 4384 0434 密码：123456

报告摘要：

In this paper, we prove the hot spots conjecture for long rotationally symmetric domains in Rn by the continuity method. More precisely, we show that the odd Neumann eigenfunction in xn associated with lowest nonzero eigenvalue is a Morse function on the boundary, which has exactly two critical points and is monotone in the direction from its minimum point to its maximum point. As a consequence, we prove that the Jerison and Nadirashvili`s conjecture 8.3 holds true for rotationally symmetric domains and are also able to obtain a sharp lower bound for the Neumann eigenvalue. This is a joint work with Prof. Hongbin Chen and Prof. Lihe Wang, which appear in Journal de Mathematiques Pures et Appliquees 2019.10.1

报告人简介：

李亦，1982年毕业于西安交通大学数学专业，获学士学位，1988年毕业于美国明尼苏达大学，获博士学位。现任美国纽约城市大学约翰杰分校学术副校长、教务长。曾任美国怀特州立大学理学及数学学院院长、爱荷华大学数学系教授及系主任、加州州立大学北岭分校教务长及副校长（学术事务）。主要研究兴趣为偏微分方程。目前任《Communication on Pure and Applied Analysis》，《Journal of Partial Differential Equations》，《 Pacific Journal of Applied Mathematics》，《Chinese Journal of Mathematics》，《 Journal of Applied Mathematics and Statistics》等国际学术刊物的编委。在国际期刊《Communications on Pure and Applied Mathematics》，《Proceedings of the Royal Society of Edinburgh Sect. A》,《J. Dynam. Differential Equations》，《Comm. Partial Differential Equations》等上发表学术论文100余篇。