偏微分方程(二)

The first goal of this course is to introudce to our students the theory of parabolic equation. In the meantime, the theory of distribution and the theory of Fourier-Transform will be introduced. Finally, we will introduce advanced techniques in the treatment of the regularity problem of elliptic equation, such as the Nash-Moser-De Giorgi method. If time permits, we will also discuss basic properties of wave equations.

A student taking this course should have basic working knowledge in Real Analysis, linear algebra, and multi-variable calculus. Basic understanding of the theory of Sobolev space and functional analysis is preferred.

Homework (20%) Attendance(30%) Oral and written report (30%) Take home final (20%)