2025.12.6 19:00--19:50 报告一: Introduction to the Method of A-Harmonic Approximation

报告简介：The method of A-harmonic approximation is a central technique for proving partial regularity of weak solutions to nonlinear elliptic systems. By freezing the coefficients and showing that the solution is “almost A-harmonic’’ on small balls, one can approximate it by a genuinely A-harmonic function, which satisfies optimal decay estimates. The method offers an elegant alternative to blow-up arguments in partial regularity theory.

2025.12.6 20:00--20:50 报告二: Optimal partial Hölder regularity of weak solutions for nonlinear sub-elliptic systems with a drift term on the Heisenberg group

报告简介：This talk will be mainly concerned with optimal partial Hölder regularity of weak solutions for nonlinear sub-elliptic systems with a drift term in divergence form on the Heisenberg group. On the basis of a generalization of the technique of A-harmonic approximation, we prove optimal partial Hölder continuity results for vector-valued solutions of the sub-elliptic systems under super-quadratic growth conditions, as well as sub-quadratic growth conditions, respectively. The primary model covered by our analysis is the non-degenerate sub-elliptic p-Laplacian system on the Heisenberg group.

报告人简介：王家林，赣南师范大学教授，博士生导师(兼职)，研究生院副院长，首届赣南师范大学赣江英才，美国数学会特约评论员，江西省数学会理事，荣获江西省自然科学奖二等奖。主要从事偏微分方程理论及其应用研究。2014国家公派美国匹兹堡大学访学研究一年，合作导师为Juan J. Manfredi教授。目前，主持省级以上科研项目10余项(国家自然科学基金项目4项)，在Adv.Nonlinear Anal.，ComptesRendus Math., Nonlinear Anal.,J. Math. Anal. Appl., Acta Math. Sci.上发表SCI检索论文30余篇。

报告地点：腾讯会议：650-733-553