1–2 | Review of Harmonic Functions and the Perspective We Take on Elliptic PDE | |
3 | Finding Other Second Derivatives from the Laplacian | |
4 | Korn's Inequality I | |
5 | Korn's Inequality II | Problem Set 1 due |
6 | Schauder's Inequality | |
7 | Using Functional Analysis to Solve Elliptic PDE | |
8 | Sobolev Inequality I | |
9 | Sobolev Inequality II | |
10–12 | De Giorgi-Nash-Moser Inequality | Problem Set 2 due |
13 | Nonlinear Elliptic PDE I | |
14 | Nonlinear Elliptic PDE II | |
15 | Barriers | |
16–17 | Minimal Graphs | Problem Set 3 due |
18–19 | Leray-Schauder Approach to Nonlinear PDE | |
20 | Gauss Circle Problem I | |
21 | Gauss Circle Problem II | |
22–24 | Fourier Analysis in PDE and Interpolation | |
25 | Applications of Interpolation | |
26 | Calderon-Zygmund Inequality I | |
27 | Calderon-Zygmund Inequality II | Problem Set 4 due |
28 | Littlewood-Paley Theory | |
29 | Strichartz Inequality I | |
30 | Strichartz Inequality II | |
31–34 | The Nonlinear Schrödinger Equation | Problem Sets 5 and 6 due |