报告题目：Stability of the Caffarelli-Kohn-Nirenberg inequality

报告人：吴元泽教授，中国矿业大学

报告时间：2024年10月29日（周二）14:00-15:00

会议地点：腾讯会议：436-157-663

摘要：In this talk, I will report our recent results on the stability of the Caffarelli-Kohn-Nirenberg inequality both in the functional inequality setting and in the critical point setting. In these results, we establish the sharp Bianchi-Egnell stability in the functional inequality setting under the nondegenerate assumption and discuss the existence of minimizers of the variational problem related to the optimal constant. We also establish the sharp Figalli-Glaudo stability in the critical point setting both under the nondegenerate assumption and the degenerate assumption. Rather surprisingly, the optimal power of the stability under the degenerate assumption is an absolute constant which is independent of the power of the nonlinearity and the number of bubbles.

报告人简介：吴元泽，博士、教授、博士生导师，中国矿业大学青年学术带头人、数学系科研副主任。兼任第十三届江苏省数学会理事、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。发表学术论文近30篇，其中部分成果发表于《Math. Ann.》，《J. Math. Pures Appl.》，《J. Funct. Anal.》，《Calc. Var. PDEs》，《Nonlinearity》等学术刊物上。

邀请人：非线性分析与PDE团队