| 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 R2: 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 |
