Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	邓斌，武汉大学
Inviter:
Title:	Sharp quantitative estimates of Struwe’s decomposition
Time & Venue:	2022.06.15 14:00-16:00 腾讯会议：37213371800 密码：0817
Abstract:	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.