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张 翼: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)

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 张 翼，中科院数学所
Inviter:
Title:
 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)
Time & Venue:
 2021.10.13 11:00-11:30 南楼N204室
Abstract:
 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.

相关话题/数学 正则 椭圆 中科院 线性

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