Spring 2024, Math 251A

Introduction to PDEs

Time/Place: MWF at 11am in MS 5203

Office hours: Mondays 12-1, Wednesdays 10-11 or by appointment.

Textbooks: Evans, Partial Differential Equations,

Jost, PDEs,

Han and Lin, Elliptic PDEs,

Notes and research articles.

Topics to be discussed:

1. Basic linear PDEs and their properties: Chapter 2 and some of Chapter 3, Evans.

2. Elliptic equations: weak solutions, maximum principle and Harnack inequality, existence, De Giorgi-Nash-Moser iteration.

3. Lagrangian flows: The main reference is the following paper:

We will briefly review the preliminary material (e.g. Sobolev spaces) as needed in the class.

Grading is based on the completion of 5-6 homework assignments. Homework will be assigned on Thursdays and will be due the Wednesday after.

Homework Problems

Homework 1 is Here

Homework 2 is Here

Homework 3 is Here

Homework 4 is Here