数学研究所研讨班:近期在拟线性椭圆方程正则性上的若干进展 （Recent progress on the regularity of semilinear elliptic PDEs)

中科院数学与系统科学研究院

数学研究所

研 讨 班

报告人：张 翼（中科院数学所）

题  目：近期在拟线性椭圆方程正则性上的若干进展 （Recent progress on the regularity of semilinear elliptic PDEs)

时  间：2021.10.13（星期三），11:00-11:30

地  点：数学院南楼N204室

摘  要：Let u be a solution to the equation -\Delta u =f(u), where f is postive, smooth, convex, increasing and superlinear, i.e. f(t)/t goes to \infty as t\to \infty. Cabrbe-Figalli-Ros-Oton- Serra proved that, when n\le 9, any stable solution to this equation is bounded (and then smooth). In this talk we introduce the recent progress on 

 (1) sharp regularity of stable solutions when n\ge 10 and Liouville theorem; 

 (2) uniform boundedness of finite Morse index solutions when f is supercritical.