Asymptotic Expansions of Solutions of the Yamabe Equation and the sigma-k Yamabe Equation near Isolated Singular Points
偏微分方程专题报告
报告题目(Title)：Asymptotic Expansions of Solutions of the Yamabe Equation and the sigma-k Yamabe Equation near Isolated Singular Points
报告人(Speaker)：Qing Han (University of Notre Dame)
地点(Place)：后主楼1223
时间(Time)：2019年3月19日 10:00-11:00
邀请人(Inviter)：李海刚
报告摘要
We study asymptotic behaviors of positive solutions to the Yamabe equation and the sigma-k Yamabe equation near isolated singular points and establish expansions up to arbitrary orders. Such results generalize an earlier pioneering work by Caffarelli, Gidas, and Spruck, and a work by Korevaar, Mazzeo, Pacard, and Schoen, on the Yamabe equation, and a work by Han, Li, and Teixeira on the sigma-k Yamabe equation. The proof is based on a study of the linearized operators at radial solutions, following an approach adopted by Korevaar et al.
