北航学术报告

--- 分析、偏微分方程与动力系统讨论班(2025秋季第4讲)

On Brezis' First Open Problem: A Complete Solution

孙黎明（中国科学院数学与系统科学研究院）

时间：2025年09月26日（周五）下午16:00-17:00

地点：沙河国实E806

摘要: In 2023, H. Brezis published a list of his "favorite open problems", which he described as challenges he had "raised throughout his career and has resisted so far". We provide a complete resolution to the first one–Open Problem 1.1–in Brezis's favorite open problems list: the existence of solutions to the long-standing Brezis-Nirenberg problem on a three-dimensional ball. Furthermore, using the building blocks of Del Pino-Musso-Pacard-Pistoia sign-changing solutions to the Yamabe problem, we establish the existence of infinitely many sign-changing, nonradial solutions for the full range of the parameter.

报告人简介: 孙黎明，中国科学院数学与系统科学研究院副研究员，2017年博士毕业于美国罗格斯大学。2008-2021年先后在约翰霍普金斯大学和英属哥伦比亚大学担任访问助理教授。研究方向是几何分析和非线性偏微分方程，研究成果发表于Duke Math Journal., Advances in Math， J. Funct. Anal.，J. Lond. Math. Soc等重要学术期刊。

邀请人：戴蔚、彭发、彭少龙

欢迎大家参加！