北航数学论坛
---分析、偏微分方程与动力系统讨论班(2025春季第18讲)
On Brezis' first open problem: a complete solution
杨文
（澳门大学）
报告时间：2025年7月8日 星期二 上午9：00-10：00
报告地点：沙河校区国实E803
报告摘要：
In 2023, H. Brezis published a list of his“favorite open problems”, which he describes 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：杨文，澳门大学副教授，国家高层次青年人才，博士毕业于加拿大英属哥伦比亚大学，师从魏军城教授，主要从事非线性椭圆型方程的研究，已在J. Differential Geom., Arch. Rat. Mech. Anal., J. Math. Pure. App., Proc. LMS, Comm. PDEs, J. Funct. Anal. 等数学期刊发表论文50余篇。
邀请人：戴蔚
