18.152 | Fall 2005 | Undergraduate

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

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Fall 2005
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