Miguel Rodrigues
Prerequisites
The main advanced prerequisite is Sobolev spaces as covered by the course preceding it, Sobolev Spaces and Elliptic Equations. The corresponding material is also covered by
- chapters 8 and 9 of Haïm Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations;
- chapter 5 of Craig Evans, Partial Differential Equations.
The 5 minutes Lebesgue videoclip (unfortunately in French language) entitled Comment mesurer la taille d'une fonction ? also provides some insights on the latter.
Less advanced prerequisites include measure theory and integration, differential calculus and ordinary differential equations, functional analysis and elementary ditribution theory. A good way to get an overall grasp on those is to study
- appendices of Craig Evans, Partial Differential Equations.
- chapter 10 of Thomas Alazard and Claude Zuily, Tools and problems in partial differential equations.
To cover the material in details one may combine the following books
- Sylvie Benzoni-Gavage, Calcul différentiel et équations différentielles (in French);
- first twelve chapters of Walter Rudin, Real and Complex Analysis;
- first five chapters of Haïm Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations;
- Claude Zuily, Distributions et équations aux dérivées partielles (in French).
Tests
The course includes two tests: one homework (CC1), one final in-class evaluation (CC2).
The final course grade is then obtained through max((CC1+CC2)/2,CC2).
The homework is due for the course of November 29th.