Beijing Institute of Mathematical Sciences and Applications

This short course is aimed to give a basic introduction to p-harmonic functions.
I will start with introductory remarks on Sobolev spaces and derive several inequalities needed for the course. I will then mostly follow lecture notes by Peter Lindqvist "Notes on the Stationary p-Laplace Equation" Springer Briefs in Mathematics, 2019.

The plan is to cover the following topics: weak solutions for Dirichlet problem, regularity theory, differentiability and p-superharmonic functions. If time permits I will also discuss Perron's method and viscosity solutions.

Each class comprises two lecture sessions and one discussion session (for students attending in person).

The second class will be on Sep. 20th, from 3:20 p.m. to 5:50 p.m. in Shuangqing-Room A513.

Because of the National Day holiday, the fourth class will be on Sep. 26th, from 9:50 a.m. to 12:15 p.m. in Shuangqing-Room B627.