偏微分方程研讨班：Sharp quantitative estimates of Struwe’s decomposition

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)   
题  目：Sharp quantitative estimates of Struwe’s decomposition
时  间：2022.06.15（星期三）下午14:00-16:00
地  点：腾讯会议：37213371800，密码：0817
摘  要：Suppose u∈H ̇^1 (R^n).  In a fundamental paper,  Struwe proved that if u≥0 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 Struwe’s decomposition. Precisely, we proved nonlinear quantitative estimates for dimension n≥6 by Lyapunov-Schmidt reduction while Figalli-Glaudo proved a linear estimate for dimension 3≤n≤5. 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.