Mikhail Feldman: Fall 2017:
Instructor : Mikhail Feldman, Fall 2017:
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 2,3,5,6.
The course will consist of the following parts:
1. Basic properties of solutions of Laplace's equation and the heat and wave equations.
2. Sobolev spaces.
3. Second order linear elliptic equations: existence, regularity, maximum principles.
4. First order nonlinear PDE: introduction to Hamilton-Jacobi equations and conservation laws.