Hung Tran: Fall 2018.
Instructor : Hung Tran, Fall 2018.
Textbook: L. C. Evans. Partial differential equations. 2nd edition. Graduate Studies in Mathematics, 19.
American Mathematical Society, Providence, RI
Content : This is the first of two courses (math 820 being the second) on PDE. We will follow the textbook by L. C. Evans, Chapters 1, 2, 3, 5, 6.
The course will consist of the following parts:
1. Basic properties of solutions of 4 important linear PDEs: transport equations, Laplace's equation, the heat and wave equations.
2. First order nonlinear PDE: introduction to Hamilton-Jacobi equations and conservation laws.
3. Sobolev spaces.
4. Second order linear elliptic equations: existence, regularity, maximum principles.