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Non-degenerate of multiple bubbling solutions for prescribed curvature equation and applications

郭玉霞 教授(清华大学)
Friday, July 17th, 2020, 3:00 PM  腾讯会议 ID 461 708 200
主持人:王丽萍 教授
报告时间:7月17日下午15:00- 16:00
报告平台:腾讯会议 ID 461 708 200

郭玉霞,清华大学数学系教授,博士生导师,德国洪堡基金获得者。主要从事非线性泛函分析及其在偏微分方程中的应用等方面的研究工作。2002年世界数学家大会卫星会议邀请报告人。2002年以来曾先后主持完成国家自然科学基金5项,作为主要成员参与完成重点项目1项.目前参与面上项目1项, 主持面上项目1项。公开发表国际SCI论文70余篇,部分研究成果发表在国际权威数学期刊比如: Comm.Pure. Appl. Math., Jour. Diff. Equa., Comm. Parl. Diff. Equa., Cal. Var. PDE., Jour. Func. Anal., SIAM J. Contr. Opt., Pro. Lond. Math Soc, JMPA等,其研究成果被国内外专家学者广泛引用。

In this talk, I am going to consider the following prescribed scalar curvature equations in $\R^N$



- \Delta u =K(|y|)u^{2^*-1},\quad u>0 \ \ \mbox{in} \ \R^N, \ \ \

u \in D^{1, 2}(\R^N),


where $K(r)$ is a positive function, $2^*=\frac{2N}{N-2}$. We first prove a non-degeneracy result for the positive multi-bubbling solutions constructed in \cite{WY} by using the local Pohozaev identities. Then we use this non-degeneracy result to glue together bubbles with different concentration rate to obatin new solutions. This is the joint work with M.Musso, S.Peng and S.Yan.
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