报告题目：Interior and boundary isolated singularities of solutions of some elliptic equations

报告人：马世光 教授 南开大学

报告时间：2026年7月19日 星期日 下午15:00 –16:00

报告地点：伍卓群楼第二报告厅

校内联系人:任长宇[email protected]

报告摘要：

    This presentation discusses interior and boundary isolated singularities of nonnegative solutions to critical elliptic inequalities involving the Laplace and p-Laplace operators. We first recall basic theories including p-superharmonic functions, Wolff potentials, critical exponents of Lane–Emden equations, and classic results by Serrin, Taliaferro and Guedda–Veron.

    Two main problems are studied. For interior singularities of the critical p-Laplace inequality, we state joint theorem with my student Zang. All solutions fall into three cases: removable smooth extension, pure power blow-up, or logarithmic corrected blow-up with an explicit lower bound, and the ratio of the solution to its radial infimum converges to one near the origin.

   For boundary singularities on the half-space with zero boundary condition, our theorem with Dong classifies all singular behaviours into three parallel types. Key techniques include rescaling, Harnack inequalities and radial variable transformation. We also show applications to conformal geometry and list several open problems for further research.

报告人简介：

    马世光，南开大学教授、博士生导师。本科就读于脱衣舞-性感脱衣舞-性感衣舞 数学与应用数学专业，北京大学基础数学专业直博；公派赴普林斯顿大学联合培养，后于法国巴黎综合理工脱衣舞 完成博士后研究。国家 “四青” 人才，天津市杰出青年基金获得者。研究方向：几何分析、几何偏微分方程、共形几何、拟线性椭圆方程奇点理论；核心研究p-Laplace算子、Lane–Emden型不等式内部与边界孤立奇点分类，非线性位势理论及其在共形几何中的应用。 文章发表在：Adv.Math., Math.Ann., Anal.PDE., Comm.Anal.Geom.等杂志。