王长友老师报告信息
报告时间：2023年6月28日（星期三）下午4:30-5:30
报告地点：数学院207
Title: Heat flow of s-harmonic maps into spheres.
Abstract: For 0<s<1, s-harmonic maps into manifolds corresponds to the critical points of the Dirichlet s-energy of maps into manifolds $N$. The resulting Euler-Lagrange equation involves a fractional s-Laplace system with supercritical nonlinearities. While they can be viewed as a natural extension of harmonic maps, in which s=1, the analysis of s-harmonic maps tends out to be much more challenging due to the nonlocal features of the equations. In this talk, I will discuss the time-dependent s-harmonic maps, or $(\partial_t-\Delta)^s u \perp T_u N$. I will present a recent theorem on the partial regularity of suitable weak heat flow of s-harmonic maps. I will describe an existence theorem, joint with Sire and others, when s=1/2.
报告人简介：王长友教授是偏微分方程领域的知名专家，于1996年在Rice大学获得博士学位，先后在芝加哥大学，卡塔基大学，普渡大学工作。研究兴趣包括PDE，几何分析等，主持多项美国自然科学基金，获得荣誉包括：Sloan奖、美国数学会Centennial Fellowship、IMA New Directions奖、Simons Fellowship等。已在CPAM, Arch. Ration. Mech. Anal., Comm. Math. Phys., Trans. Amer. Math. Soc. 等国际高水平期刊发表论文100余篇。
