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:邓斌 (武汉大学)   
  目:Sharp quantitative estimates of Struwes decomposition
  间:2022.06.15(星期三)下午14:00-16:00
  点:腾讯会议:37213371800,密码:0817
  要:Suppose uH ̇^1 (R^n).  In a fundamental paper,  Struwe proved that if u0 and u+u^((n+2)/(n-2)) _(H^(-1) )=:Γ(u)0 then dist(u,T)0, where dist(u,T) denotes the H ̇^1-distance of u from the manifold of sums of Talenti bubbles. In this talk, I will talk about a quantitative version of this Struwes decomposition. Precisely, we proved nonlinear quantitative estimates for dimension n6 by Lyapunov-Schmidt reduction while Figalli-Glaudo proved a linear estimate for dimension 3n5. Furthermore, we showed that these estimates are sharp in the sense of the exponents are optimal. It is joint work with Liming Sun and Juncheng Wei.

 

 

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