偏微分方程研讨班：Optimal regularity and Liouville property for stable solutions to semilinear elliptic equations

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：  彭发 博士（中科院数学院）

题  目：Optimal regularity and Liouville property for stable solutions to semilinear elliptic equations

时  间：2022.04.26（星期二）15:00-16:00

地  点：腾讯会议 949 698 932

摘  要：In this talk, we will introduce a work with Yi Ru-Ya Zhang and Yuan Zhou about the regularity and Liouville property for stable solutions to semilinear elliptic equations $-\Deltau=f(u)$. When dimension $n\le 5$ and $f$ changes sign, we study the boundednees for stable solutions. When $n\ge10$ and $f\$ is nonnegative, we also give the sharp BMO regularity and Morrey regularity for stable solutions. In particular, as an application, we show a sharp Liouville property for stable solutions.