课程题目：On some inequalities of Bliss-Moser type & Nonlinearities and singularities in elliptic equations
报告人：Bernhard Ruf 教授
所在单位：Istituto Lombardo - Accademia di Scienze e Lettere, Milano
报告时间：2026年5月28日 9:00-12:30; 14:00-17:30 (lesson 1-6）
2026年5月29日 8：30-10：00 (lesson 7-8)
报告地点：正新楼105
校内联系人：魏元鸿 weiyuanhong@jlu.edu.cn
课程摘要：
On some inequalities of Bliss-Moser type （1-6）
From the Bliss inequalities, which are a generalization of the Hardy inequality, one can derive a limiting Bliss inequality, which is of Trudinger-Moser type. We then consider a critical version of this inequality, and discuss related non-compactness properties. Furthermore, we show that this inequality is related to critical boundary growth for radial functions on a disk in two dimensions. Finally, we prove the existence of solutions for associated critical boundary value problems.
Nonlinearities and singularities in elliptic equations （7-8）
We discuss applications of singularity theory to some nonlinear elliptic differential equations. We first give a short introduction of singularity theory (or catastrophe theory) in the sense of H. Whitney, R. Thom and V.I. Arnold in finite dimensions and discuss the extensions to Banach spaces. We then consider elliptic equations with nonlinearities which interact with an eigenvalue of the linear operator and classify the singularities. For certain equations this allows to give a complete characterization of the solution geometry and to determine the exact number of solutions.
报告人简介：
Bernhard Ruf教授是国际知名的数学家，现任意大利米兰大学数学学院教授，并任意大利伦巴第科学与文学院院士。他的研究领域主要集中在非线性分析、非线性偏微分方程、变分法以及奇点分岔理论。
