Differential Analysis II: Partial Differential Equations and Fourier Analysis

Lecture Notes

Course Summary (PDF)

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.)