Report Title：On some inequalities of Bliss-Moser type & Nonlinearities and singularities in elliptic equations
Reporter：Professor Bernhard Ruf
Affiliation: Istituto Lombardo - Accademia di Scienze e Lettere, Milano
Report Time: 9:00-12:30, 14:00-17:30 May 28, 2026(lesson 1-6); 8:30-10:00 May 29, 2026 (lesson 7-8)
Report Location: Room 105, Zhengxin Building
University Contact: Wei Yuanhong (weiyuanhong@jlu.edu.cn)
Abstract:
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.
Bio:
Professor Bernhard Ruf is an internationally renowned mathematician. He currently holds the position of professor at the School of Mathematics, University of Milan, Italy, and is also a member of the Lombardy Academy of Sciences and Letters, Italy.
