Report Title：The nonlinear p-curl-curl problem (1-10)
Reporter：Professor Jarosław Mederski
Affiliation: Institute of Mathematics, Polish Academy of Sciences
Report Time:
13:00-14:30 February 7,2026 (lesson 1-2)
14:40-16:10 February 7,2026(lesson 3-4）
16:20-17:50 February 7,2026(lesson 5-6)
8:00-9:30 February 8,2026(lesson 7-8）
9:40-11:10 February 8,2026(lesson 9-10)
Report Location: Room 311, Zhengxin Building
University Contact: 467718116@qq.com
Abstract:
Nonlinear curl-curl problems have recently emerged in the study of exact electromagnetic wave propagation in nonlinear media modeled by Maxwell’s equations. For example, the quintic effect leads to a critical partial differential equation involving the curl-curl operator. Ground state solutions of this problem are related to the optimizers of a new Sobolev-type inequality. We present recent results concerning the existence of ground state solutions and discuss certain symmetry properties of the problem. Applications to zero modes of the Dirac equations will also be considered. This is a joint work with Andrzej Szulkin.
Bio:
Jarosław Mederski, a professor at the Polish Academy of Sciences, primarily specializes in the study of partial differential equations, particularly variational methods related to the Schrödinger equation and nonlinear field equations.
