数学系学术报告-Non-degeneracy and Existence of Bubbling Solutions for Fractional Laplacian Problems
作者:   发布时间:2021-04-13   访问次数:10

报告人: 郭玉霞  教授

单位:清华大学数学科学系

时间:2021416日下午13:30-14:30

腾讯 ID: 521 465 762

报告题目: Non-degeneracy and Existence of Bubbling Solutions for Fractional Laplacian Problems

 

报告摘要:


In this talk, we consider the following equation involving Fractional Laplacian operator:


(P)

where, s>,  Ω is a bounded domain in , N>2s.We first show that if λ>0 is small, single bubbling solutions of (P) concentrating at a non-degenerate critical point of the Robin function is non-degenerate provided N>4s+1. Then, as an application the nondegeneragy obtained above, we prove that if N∈ [4s+1, 6s] and Ω is a ball, (P) has infinitely many sign-changing bubbling solutions, whose energy can be arbitrarily large.


报告人简介: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,面上项目1项. 目前参与重点项目1项, 主持面上项目1项。公开发表国际SCI论文80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., JMPA, Jour. Func. Anal., Comm. Parl. Diff. Equa.,  Cal. Var. PDE., Jour. Diff. Equa., SIAM J. Contr. Opt., Pro. Lond. Math Soc, 等,其研究成果被国内外专家学者广泛引用。