学术报告

--- 分析、方程与动力系统讨论班(2026春季第9讲)

Symmetry of nonnegative weak solutions to a class of quasilinear elliptic equations

詹伟城 副教授

(厦门大学)

时间与地点：6月17日（周三）10:00-11:00（北京时间)

沙河校区国实E806

摘要: In this talk, I will present several recent symmetry results for nonnegative weak solutions to a broad class of quasilinear elliptic equations, with particular emphasis on equations of $p$-Laplace type. We first extend the classical Gidas-Ni-Nirenberg  theorem to the quasilinear setting of $p$-Laplace type equations. Under very mild assumptions on the nonlinear term, we then prove that every nonnegative weak solution is necessarily radially symmetric and radially nonincreasing, thereby giving an affirmative answer to a question raised by P.-L. Lions in 1981. We also establish analogous symmetry results in annular domains. Finally, I will discuss several related symmetry and rigidity phenomena arising in overdetermined elliptic problems.

报告人简介: 詹伟城，男，厦门大学数学科学学院副教授。主要从事非线性泛函分析理论与方法的研究，重点探索其在流体力学数学理论中的应用，相关成果发表在Ann. PDE, TAMS, Math Ann, JFA, IMRN, SIMA等学术期刊。

邀请人：戴蔚  彭发  彭少龙

欢迎大家参加！