中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：李一超  (北京大学)   

题  目：Asymptotic Expansions of Solutions of the Yamabe Equation near Isolated Singular Points

时  间：2022.05.25（星期三）下午2:00-4:00

地  点：腾讯会议：372-1337-1800，密码：0817

摘  要：We study asymptotic behaviors of positive solutions to the Yamabe equation near isolated singularities 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. Then, we study the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high order of approximation. This talk is based on joint works with Qing Han and Xiaoxiao Li.