报告题目：Construction of bubbling solutions of the Brezis-Nirenberg problems in 4D and 5D general bounded domains

报 告 人：吴元泽 教授（云南师范大学）

报告时间：2025年5月29日（星期四）10:00-11:00

报告地点：数学大楼914

参加人员：教师、研究生、本科生

报告摘要：In this talk, we will report our recent results on the Brezis-Nirenberg problem. We prove that every eigenvalue of the Laplacian operator with the Dirichlet boundary is a concentration value of the 4D and 5D BN problem by constructing bubbling solutions with precisely asymptotic profiles via the Ljapunov-Schmidt reduction arguments. Our results suggest that the bubbling phenomenon of 4D and 5D BN problem as the parameter is close to the eigenvalues are governed by crucial functions related to the eigenfunctions, which has not been observed yet in the literature to our best knowledge. Moreover, as the parameter is close to the eigenvalues, there are arbitrary number of multi-bump bubbing solutions in 4D while, there are only finitely many number of multi-bump bubbing solutions in 5D, which are also new findings to our best knowledge.

报告人简介：吴元泽，博士、云南师范大学教授、博士生导师，美国数学会《Mathmatical Reviews》评论员。获第八届江苏省数学成就奖。主要研究领域为非线性分析和非线性椭圆型偏微分方程（组）。现主持国家自然科学基金面上项目一项，主持完成国家自然科学基金青年基金、数学天元基金各1项。发表学术论文30余篇，其中部分成果发表于《Math. Ann.》《J. Math. Pures Appl.》《J. Funct. Anal.》，《Calc. Var. PDEs》《Nonlinearity》等学术期刊。