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Introduction to Partial Differential Equations >> Content Detail



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LEC #TOPICS
1Harmonic Functions and the Harnack Inequality
2The Gradient Estimate
3The Hopf Maximum Principle
4The Poincare Inequalities
5The Cacciopolli Inequality
6More General Operators
7Consequences of Cacciopolli
8Maximum Principles and Gradient Estimates
9Hopf and Harnack for L-harmonic Functions
10An Improved Gradient Estimate for Harmonic Functions
11More on Harmonic Functions on a Ball
12Solving the Laplace Equation in R2: The Dirichlet Problem
13The Heat Equation
14A Gradient Estimate for the Heat Equation on a Ball
15Campanato's Lemma and Morrey's Lemma
16Five Inequalities for Harmonic Functions
17Regularity of L-harmonic Functions Part I
18Regularity of L-harmonic Functions Part II
19Regularity of L-harmonic Functions Part III
20Smoothness of L-harmonic Functions
21The Mean Value Inequality Revisited Part I
22The Mean Value Inequality Revisited Part II
23Moser's Approach

 








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