Fall 2026, Math 251A

Introduction to PDEs

Time/Place: MWF at 11am (?)

Office hours: TBA

Textbooks: (Main) Evans, Partial Differential Equations.

J. Jost, PDEs.

Topics to be discussed:

1. Basic linear PDEs and their properties: Chapter 2 of Evans.

2. Hamilton-Jacobi equation and Conservation law: Chapter 3 of Evans.

3. Elliptic and Parabolic equations: maximum principle, existence, uniqueness, stability: Evans and Jost.

4. Viscous Hamilton-Jacobi equation and Optimal control theory: Chapter 10 of Evans.

5. Sobolev spaces: Chapter 5 of Evans.

6. (If time permits) Lagrangian flows: The main reference is the following paper:

The course requires some exposure to basic measure theory. We will also go through some material from measure theory as needed in the class.

Grading is based on the completion of 4-5 homework assignments.

Homework problems