Introduction to Partial Differential Equations

Calendar

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 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