题目：Some Results on the Conformally Invariant Equations of Fourth Order

报告人：黄侠 副研究员（华东师范大学）

地点：腾讯会议室（详见网页）

时间：2020年6月23日 10:00-11:00

摘要：I will talk about the weighted equation

$$/Delta(|x|^{-/alpha}/Delta u)=|x|^{/beta}u^p {in}~ /mathbb{R}^n/backslash{/{0}/},

$$ where $n/geq5, -n</alpha<n-4$ and $(p, /alpha,/beta, n)$ belongs to the critical hyperbola with $p>1$ and $$/frac{n+/alpha}{2}+/frac{n+/beta}{p+1}=n-2.$$ First, we give the classification to the positive solutions. It is also closely related to the Caffarelli-Kohn-Nirenberg inequality, and we get some fundamental results such as the best embedding constants, the existence and nonexistence of extremal functions, and their qualitative properties. It's well-known that for $p=1$, it's relate to the Hardy-Rellich inequality, at last if time permits, I also will report new results of Hardy -Rellich Inequalities via Equalities and application of Hardy-Rellich Inequalities with remainder terms in stability.

参会方式: 加入腾讯会议：

https://meeting.tencent.com/s/wZsc8lLPIv2J

ID：812 489 155

All are welcome!