Differential Analysis II: Partial Differential Equations and Fourier Analysis

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