Calendar

SES # TOPICS KEY DATES
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