| SES # | TOPICS |
|---|---|
| 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.) |