School of Mathematical Sciences Academic Report [2025] No. 043  

(High-Level University Construction Series Report No. 1065)  

Lecture Title: A Class of Coupled Obstacle Systems

Speaker: Wang Cong (Southwest Jiaotong University)  

Date & Time: 9:00–10:00 AM, May 23, 2025  

Venue: Room 426, Huixing Building  

Abstract: In this talk, Dr. Wang Cong will present recent research on the regularity of solutions and free boundary regularity in obstacle problems. The focus is on a class of coupled obstacle systems modeling cooperative and competitive interactions, which are formed by two equations derived from classical obstacle problems. Using the theory of constrained minimization in variational methods, the existence of solutions to the system is established, and optimal regularity of the solutions is obtained. Further, as the coefficient γ→0, it is proven that there exists a sequence of solutions converging to the solution of a single classical obstacle equation. Inspired by ideas from single classical obstacle problems, the regularity of free boundaries—particularly at regular and singular points—is investigated using blow-up analysis, Weiss-type monotonicity formulas, and Monneau-type monotonicity formulas. These techniques shed light on the geometric and analytical properties of free boundaries in coupled systems.

Biography: Wang Cong received her Ph.D. from Capital Normal University and completed postdoctoral research at Sichuan University. Her research focuses on partial differential equations and functional analysis. She has published more than ten papers in domestic and international mathematical journals, including Journal of Differential Equations，Advanced Nonlinear Studies，Journal of Mathematical Physics，Mathematical Methods in the Applied Sciences.

All faculty and students are welcome to attend!

Invited by: Huang Lanxin

School of Mathematical Sciences  

May 22, 2025