20220816 郑高峰 $L^p$ regularity theory for even order elliptic systems with antisymmetric first order potentials

报告人：郑高峰

邀请人：李沁峰

报告时间：2022年8月16日下午4:00-5:00（星期二）

报告地点：必赢76net线路唯一官方网站数学院425报告厅

报告题目：$L^p$ regularity theory for even order elliptic systems with antisymmetric first order potentials

摘要：In this talk, we are concerned with the optimal interior regularity theory to the system $$\Delta^{m}u=\sum_{l=0}^{m-1}\Delta^{l}\left\langle V_{l},du\right\rangle +\sum_{l=0}^{m-2}\Delta^{l}\delta\left(w_{l}du\right) +f \qquad \text{ in } B^{2m}.$$ Combining the conservation law established by Longueville-Gastel for homogeneous system and some new ideas together, we obtain optimal H\"older continuity and sharp $L^p$ regularity theory, similar to that of Sharp and Topping in two order case, for weak solutions to the above inhomogeneous system. Our results can be applied to study heat flow and bubbling analysis for polyharmonic mappings. This is a joint work with Prof. Chang-Yu Guo and Prof. Chang-Lin Xiang.

报告人简介：郑高峰，华中师范大学数学与统计学学院教授，主要从事偏微分方程、几何发展方程的研究。曾主持多项国家自然科学基金，在J. Math. Pures Appl., J. Funct. Anal., Calc. Var. PDE等杂志上发表学术论文二十余篇。