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Introduction to Partial Differential Equations >> Content Detail



Lecture Notes



Lecture Notes

The lecture notes for this course were prepared by Dale Winter, a student in the class, in collaboration with Prof. Colding.


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

 








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