报告题目：The Critical Semilinear Elliptic Equation with Isolated Boundary Singularities

报告人：王华阳，北京师范大学

报告时间：2026年9月20日（周日）14:00-16:00

报告地点：20-306

报告摘要：Continuing the work of Xiong (2017), we study the Sobolev critical semilinear elliptic equation in the half-space with an isolated boundary singularity and zero Dirichlet boundary condition. This talk addresses two open questions in this setting: the existence of Delaunay type log-periodic solutions posed by del Pino--Musso--Pacard (2007), and the asymptotic classification of singular solutions posed by Bidaut-V\'eron--Ponce--V\'eron (2007). We establish a global branch of positive log-periodic solutions along which blow-up occurs at a uniquely determined period. We also construct the corresponding concentrating family and prove its local uniqueness. Consequently, the expected stationary asymptotic classification fails, and no universal critical scaling invariant upper bound can hold throughout the half-space. This behavior contrasts sharply with the classical interior singularity theory of Caffarelli--Gidas--Spruck (1989). This is a joint work with Prof. Jingang Xiong.

报告人简介：王华阳，博士毕业于中国科学院数学与系统科学研究院，目前在北京师范大学担任励耘博士后，研究方向为非线性分析与偏微分方程，特别关注非线性Dirac方程、伪相对论方程、Hartree方程等非线性方程解的存在性、正则性、渐近行为等性质，在CVPDE、JDE、Nonlineaity、JGA等国际期刊上发表多篇学术论文。

邀请人：徐甜