走向现代数学学术报告 - 李沁峰副教授（No. 852)

报告题目：Recent progress on some mathematical problems from thermal insulation background

报告时间：2025年11月6日 14:30

腾讯会议ID：227-394-656

报 告 人：李沁峰 副教授（湖南大学）

邀 请 人：王大斌，谢华飞

报告摘要：In this talk, we will first introduce two geometric variational problems from thermal insulation background, and we will then present some qualitative and quantitative results on the optimal distribution of thermal insulation materials. When the material tends to zero, the first problem goes back to Saint-Venant theory. Then, we obtain the optimal distribution on triangular domains and narrow domains, and we also disprove the Saint-Venant conjecture via shape deformation point of view. If time permits, we will also discuss the case of Robin boundary condition, where many distinct geometric properties emerge when compared to the Dirichlet case. The talk is based on joint works with Yong Huang, Qiuqi Li, Juncheng Wei, Shuangquan Xie, Hang Yang and Ruofei Yao.

报告人简介：李沁峰，湖南大学副教授，博士生导师。2018年博士毕业于普渡大学，2018年至2020年在德州大学圣安东尼奥分校从事博士后研究。主要研究领域为几何测度论以及其在几何变分问题的应用、椭圆特征值理论和半线性椭圆方程，部分论文发表在Science China Math、Math. Ann., J. Math. Pures Appl、Indiana Univ. Math. J.、Int. Math. Res. Not.、Math. Z. 、Calc. Var. Partial Differential Equations、Adv. Calc. Var.等国际知名期刊上。先后主持国家自然科学青年项目(B类)、面上项目及青年项目(C类)，参与一项国家重点研发项目。