The lecture notes for this course were prepared by Dale Winter, a student in the class, in collaboration with Prof. Colding.
LEC # | TOPICS |
---|---|
1 | Harmonic Functions and the Harnack Inequality (PDF) |
2 | The Gradient Estimate (PDF) |
3 | The Hopf Maximum Principle (PDF) |
4 | The Poincare Inequalities (PDF) |
5 | The Cacciopolli Inequality (PDF) |
6 | More General Operators (PDF) |
7 | Consequences of Cacciopolli (PDF) |
8 | Maximum Principles and Gradient Estimates (PDF) |
9 | Hopf and Harnack for L-harmonic Functions (PDF) |
10 | An Improved Gradient Estimate for Harmonic Functions (PDF) |
11 | More on Harmonic Functions on a Ball (PDF) |
12 | Solving the Laplace Equation in R^{2}: The Dirichlet Problem (PDF) |
13 | The Heat Equation (PDF) |
14 | A Gradient Estimate for the Heat Equation on a Ball (PDF) |
15 | Campanato’s Lemma and Morrey’s Lemma (PDF) |
16 | Five Inequalities for Harmonic Functions (PDF) |
17 | Regularity of L-harmonic Functions Part I (PDF) |
18 | Regularity of L-harmonic Functions Part II (PDF) |
19 | Regularity of L-harmonic Functions Part III (PDF) |
20 | Smoothness of L-harmonic Functions (PDF) |
21 | The Mean Value Inequality Revisited Part I (PDF) |
22 | The Mean Value Inequality Revisited Part II (PDF) |
23 | Moser’s Approach (PDF) |