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