On properties of solutions to fractional and higher order systems

Abstract

In this talk, we introduce some recent results on properties of solutions to fractional and higher order systems. For instance, the classification of solutions to conformally invariant systems with mixed order and exponentially increasing or nonlocal nonlinearity, and the uniform a priori estimates for positive solutions to the n-th order superlinear Lane-Emden system in bounded domains with Navier boundary conditions in R^n (n>=3). This is joint work with Guolin Qin and Leyun Wu.

Speaker

戴蔚，北京航空航天大学数学科学学院副教授，基础数学系主任，博士生导师。2012年博士毕业于中国科学院数学与系统科学研究院，曾赴美国UC Berkeley与法国Université Sorbonne Paris Nord做访问学者。主持国家自然科学基金三项，2022年获国家自然科学基金优秀青年科学基金项目资助。主要研究分数阶与高阶椭圆方程、发展方程及多线性调和分析。相关研究结果发表在包括Adv. Math.、Analysis & PDE、IMRN、Trans. AMS、JFA、SIAM J. Math. Anal.、CVPDE、J. Anal. Math.等在内的重要学术期刊。