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 R2: 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) |
