Course No.：2802Z
Period：10
Credits：0.5
Course Category：Lecture
Primary Coverage:
There are five 2 hours lectures in this class. Each lecture consists of 90 minutes presentation, 20 minutes discussions and 10 minutes break.
1: Introduction to Sobolev Spaces.
Sobolev spaces are the basic tools in the analysis of PDEs. It’s like bricks to the buildings. Distributions and density theorems will be studied here.
2: Sobolev Embeddings and Hardy-Littlewood-Sobolev inequalities.
These estimates connect various spaces like the cement glues together the bricks. In this and the previous lectures, many detailed proof will be left to the students due to time limits. Main ideas and key methods will be presented.
3: Maximum principles and some elementary applications.
Many different form of maximum principles will be studied.
4: The method moving planes.
This method can be regarded as an elegant way of applying various kinds of maximum principles. Main emphasize will be on its applications.
5: Further applications.
The central example is the a priori estimate of solution of the prescribing scalar curvature equations where all the previous lectures come together.
Author：Congming Li 
