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This course provides a solid introduction to Partial Differential Equations for advanced undergraduate students.
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1
English
English [CC]
FREE
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Description
The focus is on linear second order uniformly elliptic and parabolic equations.
Course content
- Harmonic Functions and the Harnack Inequality Unlimited
- The Gradient Estimate Unlimited
- The Hopf Maximum Principle Unlimited
- The Poincare Inequalities Unlimited
- The Cacciopolli Inequality Unlimited
- More General Operators Unlimited
- Consequences of Cacciopolli Unlimited
- Maximum Principles and Gradient Estimates Unlimited
- Hopf and Harnack for L-harmonic Functions Unlimited
- An Improved Gradient Estimate for Harmonic Functions Unlimited
- More on Harmonic Functions on a Ball Unlimited
- Solving the Laplace Equation in R2: The Dirichlet Problem Unlimited
- The Heat Equation Unlimited
- A Gradient Estimate for the Heat Equation on a Ball Unlimited
- Campanato’s Lemma and Morrey’s Lemma Unlimited
- Five Inequalities for Harmonic Functions Unlimited
- Regularity of L-harmonic Functions Part I Unlimited
- Regularity of L-harmonic Functions Part II Unlimited
- Regularity of L-harmonic Functions Part III Unlimited
- Smoothness of L-harmonic Functions Unlimited
- The Mean Value Inequality Revisited Part I Unlimited
- The Mean Value Inequality Revisited Part II Unlimited
- Moser’s Approach Unlimited
Instructor
Massachusetts Institute of Technology
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