| 1–2 |
Review of Harmonic Functions and the Perspective We Take on Elliptic PDE (PDF) (This file is transcribed by Kevin Sackel. Used with permission.) |
| 3 |
Finding Other Second Derivatives from the Laplacian (PDF) (This file is transcribed by Cole Graham. Used with permission.) |
| 4 |
Korn's Inequality I (PDF) (This file is transcribed by Paul Gallagher. Used with permission.) |
| 5 |
Korn's Inequality II (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 6 |
Schauder's Inequality (PDF) (This file is transcribed by Paul Gallagher. Used with permission.) |
| 7 |
Using Functional Analysis to Solve Elliptic PDE (PDF) (This file is transcribed by Cole Graham. Used with permission.) |
| 8 |
Sobolev Inequality I (PDF) (This file is transcribed by Paul Gallagher. Used with permission.) |
| 9 |
Sobolev Inequality II (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 10–12 |
De Giorgi-Nash-Moser Inequality (PDF) (This file is transcribed by Paul Gallagher. Used with permission.) |
| 13 | Nonlinear Elliptic PDE I (PDF) |
| 14 |
Nonlinear Elliptic PDE II (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 15 |
Barriers (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 16–17 |
Minimal Graphs (PDF) (Courtesy of Spencer Hughes. Used with permission.) |
| 18–19 | Leray-Schauder Approach to Nonlinear PDE [no lecture notes] |
| 20 |
Gauss Circle Problem I (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 21 |
Gauss Circle Problem II (PDF) (This file is transcribed by Kevin Sackel. Used with permission.) |
| 22–24 |
Fourier Analysis in PDE and Interpolation (PDF) (This file is transcribed by Kevin Sackel. Used with permission.) |
| 25 |
Applications of Interpolation (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 26 |
Calderon-Zygmund Inequality I (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 27 |
Calderon-Zygmund Inequality II (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 28 |
Littlewood-Paley Theory (PDF) (This file is transcribed by Jane Wang. Used with permission.) |
| 29 | Strichartz Inequality I (PDF) |
| 30 |
Strichartz Inequality II (PDF) (This file is transcribed by Cole Graham. Used with permission.) |
| 31–34 |
The Nonlinear Schrödinger Equation (PDF) (This file is transcribed by Kevin Sackel. Used with permission.) |
