Abstract: In many important geometric PDEs, solutions are not necessarily regular. When the singularity occurs, we still intend to explore whether solutions possess regularity of a certain degree. The structure of the singular sets, where solutions become singular, play an important role. In this talk, we focus on two cases: the singular sets are isolated or the boundary of domains where solutions are defined. To study the regularity of solutions near the singular sets, we investigate asymptotic expansions of solutions.
 

Biography: Prof. Qing Han got his PhD from Courant Institute in 1993. After that, he was a Dickson Instructor at University of Chicago. He became a faculty member of University of Notre Dame in 1994. He was recognized by a Sloan Foundation Research Fellowship in 1999. His research interest is partial differential equations and geometric analysis.