Introduction to partial differential equations（楚健春）

This course is an introduction to the study of second order elliptic partial differential equations. We will focus on linear theory. Topics that will likely be covered include:

Lecture 1-2   Laplace's equation (Fundamental solutions, Green's function, Poisson integral formula, Dirichlet problem in balls)

Lecture 3      Harmonic functions (Mean value property, Interior estimates of derivatives, Liouville theorem, Harnack inequality)

Lecture 4-5   Maximum principle (weak maximum principle, Hopf Lemma, strong maximum principle)

Lecture 6-7   Poisson's equation (Holder spaces, Newtonian potential, Dirichlet problem in balls)

Lecture 8-10 Schauder theory (Interpolation inequalities, Schauder estimates, Dirichlet problem in domains)

楚健春，美国西北大学助理教授。2017年博士毕业于北京大学。主要研究复流形上的几何分析。