Partial Differential Equations
Students must become acquainted with the more usual methods
in linear partial differential equations and be aware of its main applications.
Luís Manuel Trabucho de Campos
Weekly - 4
Total - 14
Background in Functional Analysis and Differential Equations.
- L.C. Evans, Partial Differential Equations. American Mathematical Society.
- H. Brezis, Analyse Fonctionnelle: théorie et applications. Masson.
- D. Gilbarg & N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer.
- J.-L. Lions & E. Magenes, Nonhomogeneous boundary value problems and Applications, vol.I a III. Springer
Home work done by the student
1.Introduction to the Theory of Distributions
2. L^p spaces
3. H^m spaces
4. H^m_0 spaces
5. Hahn-Banach theorem
6, Poincaré''s Inequality
7. Sobolev theorem
8. Variational formulation of an elliptic problem
9. Lax-Milgram theorem
10. Fractional spacews
11. Trace theorem
12. H^(-m) spaces
Programs where the course is taught: